ML17300A532

Test Rept on Slender Walls

ML17300A532
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Site:	Palo Verde
Issue date:	09/30/1982
From:	AMERICAN CONCRETE INSTITUTE, STRUCTURAL ENGINEERS ASSOCIATION OF SOUTHERN CALIFORN
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Text

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//i Southern California Chapter American Concrete Institute gaHlg~

X CDUIO0NIA Structural Engineers Association of Southern California ACI-SEASC Task Committee on Slender Walls Bs09zeosso Bs09s9 PDR ADOCK 05000528 P

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American Concrete Institute, Southern California Chapter and the Structural Engineers Association of Southern California REPORT OF THE TASK COMMITTEE ON SLENDER WALLS William M. Simpson, S.E.

Chairman Samy A. Adham, C.E.

James E. Amrhein, S.E.

John Coil, S.E.

Joseph A. Dobrowolski, C.E.

Ullrich A. Foth, S.E.

James R. Johnson, S.E.

James S. Lai, S.E.

Donald E. Lee, S.Z.

Ralph S.

McLean, S.E.

Lawrence G. Selna, S.E.

Robert, E. Tobin, S.E.

Ralph S.

McLean, S.E.

Project Director February 1980 - September 1982 Los Angeles, California

Technical Editor for this report J.W. Athey Design engineers or architects using the information in this report are cautioned to exercise judgment in its application to

, individual buildings.

Specific conditions such as openings in

walls, expansion or contraction of the concrete, roof, floor or foundation details, the dynamic effects of seismic loads, as well as job site controls must all be considered.

This report is proposed for guidance

only, and the Structural Engineers Association of Southern California and the Southern California Chapter of the American Concrete Institute, including the members of the Task Committee on Slender

Walls, take no responsibility for the application of any statements or princi-ples included in this report.

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k'ABLE OF CONTENTS Section 1I~ 'I 4

4 4.2 4.3 Loading Frame Pin Connections GENERAL

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1.1 Committee Formation and Goals 1.2 Test Specimens and Results 1.3 Report of the Task Committee 1.4 Information Available MATERIALS AND MATERIAL PROPERTIES 2.1 Introduction

~C 2.2 Concrete 2.3 Concrete Block 2.4 Clay Brick 2.5 Clay Block 2.6 Mortar 2.7 Grout 2.8 Reinforcing Steel 2.9 Field Cut Prisms and Cores CONSTRUCTION OF TEST SPECIMENS 3.3.

General 3.2 Panel Descriptions 3.3 Concrete Panel Construction 3.4 Masonry Panel Construction 3.5 Placement of Steel TEST EQUIPMENT AND TEST METHODS 4.1 General

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Pacae 1-3 1-3 2-1 2-1 2-1 2-2 2"3 2-4 2-4 2-5 2-6 3<<1 3-1 3-3 3-3 3-6 4-1 4-1 4>>1 4.5 4.6 Safety Cables Loading Methods Panel Emplacement 4 4

CONTENTS (Continued)

Section 4.7 Air Pressure Measurement 4.8 Deflection Measurements 4.9 Load Control 4.10 Testing Routine TEST RESULTS Pacae 4-6 4-10 4-12 5-1 5.1 5.2 Concrete Masonry Panels Clay'rick Clay Block Masonry 5-1 5-3 5.4 Concrete Tilt-Up Walls INTERPRETATION OF TEST RESULTS 6.1 General Performance 6.2 Load-Deflection Curves 6.3 Air Bag Contact Area 6.4 Cracking Pattern 6.5 Rebound 6.6 Secondary Moments Due to Deflections (Ph Effect)

6. 7 Axial Force-Moment 1eraction diagrams 6.8

'Predictions of Deflections Using Moment/

Curvature Relationships 5-3 6-1 6-1 6-1 6-5 6-7 6-10 6-12 "6-Z'5 6-3.9 DEVELOPMENT OF DESIGN METHODS 7.1 Introduction 7-1 7.2 7.3 7.4 7.5 Design Variables Strength and Deflection Characteristics Strength and Deflection Design Criteria Determination of ) Factor and Cracking Moments from Experimental Data 7~3 7~3 7-l7 I 3.v

CONTENTS (Concluded)

Section DESIGN EXAMPLES 8.1 Introduction 8.2 Design Examples Using Ph, Design Method 8.3 Design Examples Using SEAOSC Yellow Book Method

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CONCLUS IONS, RECOMMENDATIONS, AND OTHER CONSIDERATIONS Pacae 8-1 8<<1 8-2 8-10 9-1 10 10.1 10.2 Committee Membership Test Site 10.3 Contributors 10.4

.10.5 10.6 Documentary Film Staff Support Volunteers 10.7 References 9.3.

Conclusions 9.2 Recommendations 9.3 Other Considerations ACKNOWLEDGMENTS AND REFERENCES

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9-1 9>>2 9-3 10-1 10-1 10-1 10-2 10-3 10-3 10-3 10-5

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SECTION 1 GENERAL The increased use of concrete and masonry walls for commercial and industrial buildings is due principally to their economy, fire safety, architectural appearance, and ease of con-struction.

Along with this increased

usage, there has been a

trend toward making these walls more slender in the interest of further cost savings.

The proper design of these walls for strength and safety has been an important task for Me structural engineer,

-and a number of concepts have been developed for these walls to resist seismic or wind forces.

In conjunction with the design process, building codes have limited the ratio of height to thickness of these walls.

l. 1 COMMITTEE FORMATION AND GOALS To confirm these design concepts and to evaluate the slen-derness limitations, a volunteer committee called the ACI-SEASC Task Committee on Slender Walls was formed.

The committee consisted of representatives from the Structural Engineers Association of Southern California and the Southern California Chapter of the American Concrete Institute.

The goal of the Task Committee was to test slender concrete and masonry walls to determine their behavior when subjected to eccentric axial and lateral forces that simulated gravity loads, along with wind or seismic pressures.

1.2 TEST SPECIMENS AND RESULTS A total of 30 full-size panels were tested.

These panels were constructed of tilt-up concrete, concrete block, clay brick, and clay blocks.

The panels were tested in a special frame 1-1

I capable of simulating eccentric roof loads as well as lateral

forces, both applied at the same time.

Horizontal deflections of-the wall panels were measured under varying increments of load to determine the ultimate capacity of each panel.

The test results were dramatic and very informative.

The

'-" tests showed excellent behavior of all panels under severe load-ing conditions, and most importantly, showed that the arbitrary

" and fixed limitation of height to thickness ratio is inappro-priate and control should be based on strength and deflection considerations.

These t.ests proved that thin walls of &is con-struction can handle all specified code loadings for vertical and lateral forces with reserve deflection capacities far in excess of service requirements.

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1-1.

Members of the Task Committee on Slender Walls.

Ralph S

~ McLean (Proj.

Director),

James E. Amrhein, James S. Lai, William N. Simpson (Chairman),

Robert E. Tobin, Joseph A. Dobrowolski (kneeling),

Lawrence G. Selna, James R. Johnson, Samy A. Adham, John Coil, Donald E. Lee, and Ullrich A. Foth I

1-2

1.3 REPORT OF THE TASK COMMITTEE This report on the testing program follows, for the most

part, the experimental process.

Section 2 lists the materials and properties as they applied to the test program.

The succeed-ing two chapters describe the construction of the test specimens and explain the equipment and methods used to perform the testing.

, Test results and an interpretation of these results are given in

.,Sections 5

and 6.

The development of design methods includes design requirements and procedures, analysis

methods, and load/

deflection relations; these are presented in Chapter 7.

This is followed by design examples in Section 8.

Conclusions and recommendations are listed in Section 9.

The final section of the report is an expression of grati-

'"tude to all who contributed their" time and resources to make this

'",'project a success.

Section 10 also includes a bibliography.

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'4 1. 4 INFORMATION AVAILABLE Original test data, laboratory reports on materials, analyt-j~(ical procedures, and presentational

photos, slides and film of

fi,"jthe project are available.through the Office of the Structural

';,En'gineers Association of Southern California;;, 2550 Beverly Boule-

vard, Los Angeles, CA 90057.

This information can be obtained with the approval of the Board of Directors and upon payment of

'osts for duplication and administration.

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SECTION 2 MATERIALS AND MATERIAL PROPERTIES

2.1 INTRODUCTION

The materials in this test program were the normal materials used in average construction in Southern California.

Concrete was supplied by a local ready mix firm using a typical mix pro-portion for tilt-up concrete.

The concrete block and brick were from local manuf acturers and were'ypical of the basic quality found in the

-area.

No particular effort was made Co use high strength materials, although it appears from the results that the materials were of higher strength than generally specified.

The materials and their properties are described below.

2.2 CONCRETE Concrete was supplied by Consolidated Rock Products Co. from their Irwindale plant and was a five-sack per cu yd mix with a 0.67 water/cement ratio.

The mix design by Conrock consisted of the following quantities per cubic yard:

Portland cement 470 lb (5 sacks)

Washed concrete sand 1420 lb (~14 cu ft) 1-in. gravel 1815 lb (~18 cu ft)

Water 317 lb (38 gal)

Compressive strength results measured by Conrock were:

7-day compressive strength test 2282 psi 28-day compressive test 3181 psi 2-1

During the placing of the concrete tilt-up wall specimens, 16 cylinders and 6 concrete beams were made.

Test results by Twining Laboratories for laboratory specimens were as follows:

7-Day Test Compression 2300 psi Splitting tensile (average) 270 psi 28-Day Test

'Compression (average)

Modulus of ~lasticity Splitting tensile strength Modulus of rupture beam specimens 3,225 psi 3,360,000 psi 355 psi 695 psi 167-Days (job-cured)

Compressive strength

4,009 psi Modulus of elasticity 3,540,000 psi Modulus of rupture beams 520 psi The concrete tilt-up panels were provided with conventional tilt-up lifting inserts.

Two were placed in each edge and two at the top end of each panel.

All panels were cast October 3,

1980, and lifted October 15,

1980, and stored on edge with air space between panels.

The panels were lifted by the insert in the long edges to assure that the panels would not be damaged in lifting.

"'2.3 CONCRETE BLOCK The concrete masonry units (CMU) were supplied by Angelus "Block Co.,

Inc.

of Sun Valley, California, and were Grade N,

Type II, medium weight and normal strength.

Tested prisms of 0

2-2

concrete masonry units made at the time of construction demon-strated the following properties:

1 0 It 8 II 61t Compressive

Strength, fl 2460 psi 2595 psi 3185 psi Modulus of Elasticity, E

2.17 x 10 psi 1.72 x 10 psi 1.59 x 10 psi 2.4 CLAY BRICK The clay brick units Grade SW were supplied by Higgins Brick Co.

of Redondo

Beach, California.

Properties of brick prisms, shown in Figure 2-1, were as follows:

Clay Brick 9.6" 7'

II Compressive

Strength, fm 3060 psi 3440 psi Modulus of Elasticity, E

1.12 x 10 psi 1.42 x 10 psi 6

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2-1 Construction of 2-Wythe 9.6" Thick Grouted Brick Prisms.

2-3

2.5 CLAY BLOCK The 5-1/2 in. thick hollow brick units, clay block, were supplied by Mutual Materials Co. of Bellevue, Washington, and had the following properties:

Clay Block 5

5 It Compressive

Strength, f I m

6243 psi Nodulus of Elasticity, Em 2.33 x 3.0 psi 6

2.6 NORTAR The mortar was Type S of the following proportions:

one part portland

cement, one-half part

lime, and four parts sand by volume; all measurements were made with a cubic foot box initially.

After the job progressed, shovel measurements were used.

Mortar, Type S

2" x 4" Cylindrical Specimens Compressive

Strength, Standard f t Deviation 7 day 28-day 2348 psi 3361 psi 498 psi 614 psi The 7-day strengths ranged from a

low of 1305 psi to a high of 3365 psi.

The 28-day strengths ranged from a low of 2420 psi to a high of 4710 psi.

2.7 GROUT The grout was mixed on the job in the proportion of one part portland cement, three parts

sand, and two parts pea gravel, with enough water for a

slump of 8 to 10 in.

All materials were measured by volume and were mixed in a

drum mixer.

Seven-day average strengths of 43 grout specimens 4" x 4" x 8" were 2014 psi with a standard deviation of 400 psi; these ranged from 2-4

e a low of 1190 psi to a high of 2630 psi.

The 28-day strengths for 58 specimens 4" x 4" x 8" averaged 3106 psi with a standard deviation of 474 psi; these ranged from a

low of 1965 psi to a

high of 4000 psi.

2.8 REINFORCING STEEL All vertical steel was Grade 60 furnished by Bethlehem Steel and came from the same heat.

The mill reported yield strength of 72,250 psi and ultimate tensile strength of 102,750 psi.

Twining Laboratories reported the yield strength to be 67,500 psi and the ultimate tensile strength to be 102,000 psi.

The average yield strength was 70,000 psi.

Elongation in 8 in. equaled 17%.

The 6

modulus of elasticity was measured to be 28.6 x 10 psi.

All vertical bars were in full length without splices.

Steel prop-

'erties on typical stress/strain tests by Twining Laboratories and

,the Structural Laboratory of UCLA are shown in Figure 2-2.

Note f

110 ksi 100

~ f,=

70 ksi Y

28.6 X 10 ksi in./in.

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= 0.0025 to 0.0032 V

0. 05 STRAIY

0. 10

0. 15 pig.

2-2 Stress-Strain Curve for Reinforcing Steel.

2-5

that the reinforcement yield plateau strain of 0.0025 to 0.0032 in.

per in.

is a

small part of the overall steel

" elongation.

e Horizontal bars were N3, Grade 40, with the mill report

'tating yield strength of 52,730 psi and ultimate tensile

- strength of 75,910 psi.

Twining Iaboratories reported the 53 bars had yield strength of 52,000 psi and ultimate tensile strength of 79,100 psi.

The elongation in 8 in. was measured at 18% and had a modulus of elasticity of 28.0 x 10 psi.

All reinforcing steel met the requirements of ASTN A615-78 Standard Specification for Deformed and Plain Billet-Steel Bars for Concrete Reinforcement.

( 2.9 FIELD CUT PRISMS AND CORES Upon completion of the deflection test program, prisms were sawed from all of the concrete

masonry, brick, and clay block panels.-

In addition, cores were drilled from all of the concrete tilt-up panels.

These samples were made over a year after the panels were first built.

Figure 2-3 shows these cut samples ready to be transported to the testing laboratory.

A graphical comparison of the f'ompressive strengths of the original prisms tested at 28 days with those cut from the walls over one year later is shown in Figure 2-4.

As expected, the compressive strengths were greater for the year-old prisms.

However, the moduli of elasticity of the older specimens were

~ both above and below the 28-day values.

This may have been due to differences in procedure since the tests were conducted originally at one laboratory and later at. another laboratory.

In either case these differences are not significant since the values were not used in the original design calculations.

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a, Fig. 2-3 Prisms and Cores from Tested Mall Panels.

700 600 I

500 400 300 200 Xo 1000 Prepared prisms tested 0 28 days.

Cut from wall-tested O 1+ y. ar.

~B31 V 0

O 1000 2000 CI 3000 Cor'+r e rn masonry Units Brick Clay Block Fig. 2-4 Tests of i'masonry Prisms.

2-7

Compression tests of 3.70-in.-dia.

concrete cores varied between 4217 and 4862 psi with an average of 4607 psi.

These compared with 28-day average strengths of 3200 psi.

Modulus of elasticity tests were not made on these cores.

On the basis of these compression

values, the concrete had gained 44% in strength over a one-year period.

The f'trength of the concrete block m

increased 43% in one year, the clay brick 35%,

and the clay block 33%.

The exact percentages are not as important as the fact that all of tne

walls, without any exceptions, improved with age.

Continuous strain measurements were taken on saw-cut, prisms from all masonry panels.

The maximum straia levels reached prior to compressional failure are as follows:

Maximum Strain Concrete Masonry Units Brick Masonry Hollow Brick Masonry 0.0032 in./in.

0.0042 in./in.

0.0038 in./in.

e 0

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0 SECTION 3 CONSTRUCTION OF TEST SPECIMENS 3.1 GENERAL In order to obtain realistic results, full-scale specimens were tested so that proper evaluations of the slenderness

effect, the Ph effect, and the eccentric moment (Pe) effect could be

'made.

All panels concrete, clay brick, clay block, and concrete block--were built in the construction yard of Sanchez and Hernandez in Irwindale, California.

3. 2 PANEL DESCRIPTIONS All panels were 4'0" wide and 24'8"

high, and were 24'0"

'between horizontal points of support (Fig. 3-1).

The panel height of 24'8" was selected because 'it represented current con-struction trends and allowed for an evaluation of the slenderness ratios from 30 to 60 with standard materials of construction.

Many industrial and commercial buildings and storage and manu-facturing facilities are designed using approximately this height.

A total of 30 walls were built for the test program.

Twelve walls were concrete tilt-up panels, three each with thicknesses of 4-3/4",

5-3/4",

7-1/4",

and 9-1/2" resulting in nominal h/t ratios of 60, 50, 40-,

and 30 respectively.

Nine

walls, three of each thickness, were concrete masonry of 6", 8",

and 10" nominal thickness with an actual thickness of 5-5/8",

7-5/8",

and 9-5/8", for slenderness h/t ratios of 51, 38, and 30.

Six walls were clay brick masonry, three each of 7.5" thick and 9.6" thick with h/t ratios of 38 and 30.

Three walls were 5-1/2" hollow clay block units with an h/t ratio of 52.

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4 I Oll Thickness, t, varies; see panel lists.

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3ll P1 Angle 6" X 6" X 3/8" 4 bo1ts 3/4" DETAIL AT TOP OF WALL 4J Cl Cl o

~l 3 dowels f14 X 1'8" II Ii 3/~16" II 2/2" plate

~ Split 3" std. pipe DETAIL AT BOTTOM OF WALL FRONT ELEVATION a

SIDE ELEVATION Fig. 3-1 Typical Panel Details:

Concrete and Masonry.

3-2

The panels were built on half-inch base plates and supported on one-half of a 4" pipe underneath (Fig. 3-2).

This provided a

true pin connection for free rotation at the base.

This pinned end simplified calculation, as there was zero moment at the bottom.

The top support allowed the panels to rotate, and the support could move vertically to allow freedom of movement and rotation but yet prevent lateral translation.

3.3 CONCRETE PANEL CONSTRUCTION The concrete tilt-up panels, as shown in Figure 3-3, were

-cast -with -the -exterior face down and with ledger bolts protruding from the exposed face.

Each panel contained'four continuous 1/2" (44) bars in the vertical direction.

Number 3 horizontal bars spaced 2'.c.

were used in the 4-3/4" thick and 5-3/4" thick panels.

Number 4 horizontal bars spaced 2'.c.

were used in the 7-1/4" thick and 9-1/2" thick panels.

After casting, panels were lifted and stored on edge, as shown in Figure 3-4, for a period of 160 days before they were again lifted to the final vertical position on the test slab.

'3.4 MASONRY PANEL CONSTRUCTION All masonry panels were built in-place similar to normal construction

methods, as shown in. Figure 3-5.

The masonry walls were built on 1/2" base plates supported on one half of a

4" pipe.

On the 1/2" plate, five 1/2" reinforcing bar dowels were welded and extended 24" into the panel.

The panel reinforc-ing steel, five g4 bars, Grade 60, lapped the steel dowels on the base plate.

The base plate was stabilized with wedges and dry-packed with mortar to secure it from moving during construction.

The masonry panels, were solid grouted

.in 4'ifts using the techniques of delayed consolidation:

After the water was absorbed into the

masonry, the grout was consolidated, which caused it to compact completely and bond firmly to the masonry.

3-3

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Fig. 3-3 Forming of Tilt-Up Panels.

3-4

Fig. 3-4 Moving Tilt-Up Concrete Panels to Storage Area.

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3-5

All brick masonry panels were constructed with continuous vertical reinforcement consisting of five 54 bars, and horizontal reinforcement. with 53 bars spaced 4'0" apart vertically.

The panels were strengthened by reinforcing steel

rods, which were embedded in the connecting grout for the clay brick and in the core grout for the concrete and clay blocks.

Fig-ure 3-6 shows the details for vertical steel placement in alter-nate rows of masonry.

Figure 3-7 shows the completed masonry walls prior to testing.

All walls were braced temporarily to prevent tipping.

3.5 PLACEMENT OF STEEL The specimens were designed to have steel reinforcement located in the center of the panel between the outer faces.

After testing, the panels were broken apart, approximately in the middle third, and the location of the reinforcing steel was measured in relation to the loading face.

Table 3-1 presents the measurements and accuracy of the steel placement.

The last column of Table 3-1 indicates the percentage of the panel width that the reinforcing steel is off center line.

For

example, for the 9-1/2" thick concrete tilt-.up panels, reinforce-ment placement remained good, within 3% of the center line loca-tion.

But for the 7-1/4" thick and the 4-3/4" thick tilt-up concrete

panels, larger d

distances were measured to as much as 23% greater than the specified d.

For the concrete

'masonry wall panels, the steel placement ranged from 4% off center line to as much as 20% off.

This meant the steel was kept within 1/2" of the specified location.

The brick wall steel placement was 19%

and 22%

off center line in two panels, hut, only 6% off in the third, which meant 3-6

Hollow brick

+~o Concrete block 2-Wy'the brick Fig. 3-6 Arrangement of Reinforcing Steel in Concrete Block, Clay Block, and Two-Wythe Brick Panels.

3-7

that the greatest discrepancy from the specified location was more than 3/4".

Placement of steel away'rom design location may increase or decrease the capacity to resist forces depending upon where the steel is located and from which direction forces are considered.

Analysis of the results reflect this variation in the location of the steel, and design parameters have been adjusted accordingly, amounting to what is known among engineers as the

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factor.

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Fig. 3-7 Concrete Masonry and Brick Masonry Panels ln-Place Ready to be Tested.

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TABLE 3-1.

PLACEMENT OF STEEL RETViFORCEMENT Panel No.

Thickness (t), in.

Nominal Measured Distance (d) from Outer Face of Wall to Center Line tt of Steel, in.

Ave.

d Bar

//1 Bar f12 Bar 03 Bar lI4 Bar 85 Variation in d in' 2

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Cl OCo 8

9 10 1) 12 13 14 15 16 "a o 17

,o 2 18 19 lt, 20 21 22 23 24 25 26 27 "i*

28 29 30 10 10 10 9.6 9.6 9.6 7.5 7.5 7.5 5.5 5.5 5.5 9.5 9.5 9.5 7.25 7.25 7.25 5.75 5.75 5.75 4.75 4.75 4.75 9.69 9.69 9.69 7.63 7.63 7.63 5.63 5.63 5.63 9.63 9.56 9.56 7.38 7.63 7.63 5.50 5.50 5.50 9.6 9.4 9.5 7.4 7.34 7.38 6.13 5.88 6.0 4.82 4.78 4.89 4.4 4.4 4.7 4.5 4.6 3.1 3.1 3.2 3.2 3.0 3.7 3.8 4.2 4.3 4.3 3.40 3.34 3.27 3.08 3.19 3.12 3.11 3.12 3.11 3.02 3.31 3.34 3.49 3.32 3.29 4.67 5.24 4.48 4.24 4.76 4.59 4.70 4.76 4.4 4.6

'.7 4.8 3.88 4.0

4. 13 4.38 2.85 3.35 3.48 3.48 4.8 4.7 4.3 4.3 3.7 3.8 3.4 3.7 3.38 3.5 3.7 3.6 3.8 3.6 3.25 3.25 2.21 2.45 2.86 2.74 2.46 2.58 2.90 3.16 2.24 2.37 2.66

'.92 5.19 5.19 4.94 5.06 4.94 4.19 4.19 4.69 4.19 4.69 5.25 5.13 5.25 5.25 5.38 4.13 4.13 4.13 4.24 3.88 4.7 4.4 4.3 4.4 4.4 3.3 3;3 3.2 3.2 3.1 2.83 2.95

-'"3. 19

3. 19

3. 19 2.18 2.24 2.22 2.16 2.41 3.00

3. 15 2.99 2.99 3.07 5.38 5.63 5.88 5.88 6.01 5.81 5.62 5.69 5.69 5.56 5.06 4.39 5.25

4. 10 4.44 3.22

3. 07.

2.24 3.04 5.76 5.67 4.52 3.12 4.06 3.26 3.10 3.35 4.66 4.70 4.63

4. 10 3.29 4.53 3.70 3.63 3.48 2.56 2.77 2.55 4.5%

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0.40 in.

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0.28 in.

16$

0.62 in.

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0.59 in.

9'X 0.25 in.

20~

0.57 in.

8g 0.22 in.

19.54 0.94 in.

194 0.89 in.

22.5~

0.83 in.

18~

0.69 in.

6~

0.24 in..

17K 0.51 in.

11%

0.35 in.

20.5$

0.60 in.

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10%

0.40 in.

10'g, 0.38 in.

22/

0.84 in.

20%

0.63 in.

23/

0.69 in.

15$

0.48 in.

7$

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16%

0.38 in.

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=

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x 100; in. variation in d measured t 2

measured t - d average bar l/5 not used for concrete tilt-up panels 3-9

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SECTION 4 TEST EQUIPMENT AND TEST METHODS 4.1 GENERAL These tests were made to investigate the effect of lateral deflection on the stability of walls subjected to combined vertical and lateral loads.

Since the weight of a wall is an important part of the vertical load, it was necessary to test the walls in an upright position.

4. 2 LOADING FRAME A welded steel trussed frame (Fig. 4-1) was constructed for this purpose.

A secondary wooden structure of plywood was secured to the face of the frame as a backing for the air bag that supplied the lateral load.

The walls were held against the air bag using threaded rods at the four corners of the. walls and attached to the steel frame.

At the top of the

frame, a lever system placed vertical loads on the walls.

Loose safety cables attached to the top of the walls and to outriggers with pipe supports were used to prevent total collapse of the walls if rupture should occur.

Not shown in Figure 4-1 were a ladder and work platform for making wall attachments at the top, and wheels for moving the test frame from wall to wall.

4.3 PIN CONNECTIONS The rocker base of the wall (see Sec.

3.2) eliminated moment at the bottom of the walls.

The base assembly sat directly on the concrete floor slab.

At the

base, lateral pressure of. the air bag was resisted by a length of 6" x 3" x 1/4" rectangular steel tube across the outer face of the

wall, connected to threaded steel rods from each end of the tube to the steel frame.

See detail in Figure 4-4.

VERTICAL LOAD LEVER EVETE II ROLLER BEARING PLYWOOO ANO TRUSS JOIST BACICING FOR AIR BAG-I ~

II Il I"IliI'

,I I

~ I I

l LEDGER I ANGLE 8 TIE TEST SPECIMEN Fig. 4-1 Loading Frame Showing Drums of Water for Vertical Load and Air Bag for Lateral Load.

ADJUSTABLE SUPPORTS TUBULAR STEEL FRAME~

AI I

r E

I E

l I

I I

E R BAG I

I I

I I

I I

~ I r.IIIII IE R

V TIE LOA0 DRUM (WATER)

V ~

Sl DE ELEVATION OF TEST SE TUP R

~ ~

Fig. 4-2 Loading Frame Showing Scab Plywood Forming to Conform to the Loaded Panel.

r V

I

~,

c%

E lr ~-

JL~

fp PV~

E

Top Restraint Device that Allows Vertical Movement of Panel and Rotation at the Top.

Safety Chain Holds Panel to Prevent Sudden Collapse.

S P HER ICAL ROLLER BEARING

SIN, SO, STEEL TUBING I

II I 1+ II'

~

I I

I I

I I

)

I I

I Q)

LEDGER ANGLE 6 X 6XS/8 4

BOLTS 5/4 0 TO SPECIHEN THREADED ROO

/

(

TEST SPECIHEN 6

X N X I/4 STEEL TUBING~

SIN. 0 CYLINDRICAL WASHER~

(TYPICALI I

I I

i I

P~ rr/)i)"rr/'SS EH 8 LY Fig. 4-4 Ties to Test Frame.

At the top of the walls, bolts were built in to secure a

6" x 4" x 3/8" steel ledger angle used to apply eccentric vertical loads to the walls.

One-inch threaded rods tied the

'angle to 'the frame.

Because an extra wall built especially to test equipment and Iprocedures achieved unusually large deflections, important changes in attachment of the wall to frame were required.

The threaded steel rods for the top connections were attached to an assembly having a spherical roller bearing that rode on the steel bar and permitted ample vertical and angular movement.

This top assembly is shown in Figures 4-3 and 4-4.

4.4 SAFETY CABLES The safety cables consisted of a couple of loops of light

'steel cable passing through a

connection at each end of the t ledger angle and over the outriggers.

Only two of the standard height wall specimens and one shorter one ruptured, but in each case the cables and top anchorage (of the ledger angle) prevented the walls from falling.

'4. 5 LOADING METHODS Vertical Loads.

The lever system for vertical load (Fig. 4-1) was pivoted at the top of the main frame and projected out past the wall specimen.

Two lever arms were used and struts from the levers rested on the ledger angle.

Steel drums loaded

~with water were hung from the lever arms with steel cable after initial displacement readings without vertical or lateral load were made.

The quantity of water was adjusted for the desired load.

4 4

Lateral Loads.

A uniformly distributed lateral load was applied to the walls with an air bag.

The air bag consisted of a 20 mil vinyl bladder with welded seams and an outer wear-resistant cover of vinyl-coated nylon 22 oz material with sewed seams.

Dimensions of the bag were 18" x 48" and 24'n length.

Two ports were provided:

one for inflation in one edge of the b'ag and one in the opposite edge for pressure readings.

Grommeted flaps were provided at the top front and rear faces of e bag for hanging it from the outriggers.

Because the magnitudes of deflections of the loaded walls were much greater than anticipated and the unsupported edges of the bag ballooned

out, some loss of contact with the wall occurred at large deflections.

However, an investigation using the deflection curve obtained from test measurements showed that this loss of contact was negligible below the loading at which yielding of the reinforcement occurred.

This is discussed in Section 6.3.

h4.6 PANEL EMPLACEMENT I'fter casting and curing, each concrete wall was lifted by means of its edge insert ~ order Xo avoid Mgh stresses that would occur with end lifting.

The walls were stored on edge awaiting testing.

Later, when they were transported to the test.

site, they were again lifted by their edge lifts and rotated in the air by means of another line and inserts in the

.end of the panels; this careful handling ensured that premature cracking was avoided.

Masonry walls were constructed in-place as described in Section 3.4.

0 All walls were held in place with telescoping pipe bracing anchored to the floor.

Once the test frame, was in position and the wall secured to it, the bracing was removed.

Upon completion of testing, the brace was reinstalled, the test frame

removed,

and the wall in its deformed condition allowed to remain in place until a number of walls could be transported at one time.

4. 7 AIR PRESSURE MEASUREMENT In testing, the air bag was inflated by a small (1/2 Hp) compressor, which proved to be ideal.

A pressure regulator was

provided, but it was found that a small needle valve gave very good control of inflation.

Pressure in the bag was measured initially by a

double water tube manometer.

A difference of one inch of water indicated air pressure in the bag to be 5.2 lb/sq ft.

Later, after a trial period when both manometers were used, only the single tube manometer was used (Fig. 4-5).

A schematic of the pressure loading system is shown in Figure 4-6.

To verify the validity of calculating lateral load using indicated air pressure, strain gages were cemented to a machined section of the top and bottom threaded reaction rods.

Good agreement was found between loads determined by this method and those calculated by using indicated air pressure.

4.8 DEFLECTION MEASUREMENTS Displacement measurements were made at each support of the walls and at intermediate tenth points to obtain the shape of the elastic

curve, using three different methods.

In the first

method, yardsticks were attached to the walls at such points (Fig. 4-7) and their positions were observed through a transit set (Fig. 4-8) with its line of sight parallel to the wall.

This was reliable to the nearest 1/16 in.

A second method of measurement used dial gages calibrated in thousandths of an inch and with 3-in.

travel (Fig. 4-9).

A portable steel

pylon, independent of the test

frame, supported the dial gages.

The gages were connected to the wall by a nylon coated steel wire tension line so that large deflections of the

9

~

'easurement of Air Pressure.

Note U-Type Manometer to Measure Air Pressure on Right.

Straight Tube Manometer on Left as a Check.

ONE INCH OF WATER~4.2 LBS./SQ.FT.

BAG PRESSURE LINE I

I I

I I

AIR BAG 4'X24'X1.5' I

I N1 OI Z'

~II I

I I

( NEEOLE VALVE sl AIR PRESSURE 'LINE U-TUBE MANOMETER' r

I 1/2 H.P. COMPRESSOR Fig. 4-6 Schematic of Lateral Load System.

Fig. 4-7 Securing Yardstick to Side of Panel.

2 ~

1 r

Fig. 4-8 Reading Yardsticks Through Transit as Wall Deflected.

~

MAGNET LLEY, BALL BEARNQ MOUNTED 1/18'TEEL PLATE CEMENTED TO SPECIMEN WITH HOT GLUE DIAL INDICATOR.001' ALUMINUMPLATE SUPPORTED BY REFERENCE PYLON WEIGHT t

Fig. 4-9 Mounting of Dial Indicators.

CAPSTAN PULLEY ON POTENTIOMETER SHAFT PRECISION POTENTIOMETER RIGIDLY SUPPORTED ON REFERENCE PYLON 7 STRAND STAINLESS STEEL WIRE NYLON COATED ATTACHED TO WALL WITH MAGNET SIMILAR TO DIAL GAGES ELECTRICAL LEADS WEIGHT g ~s<

R1 f

V S2-~ R2 CAPSTAN CIRCUMFERENCE S INCHES; S1 ON-OFF S2-CHECK VOLTAGE To R2 R1 100 OHMS R21000 OHMS 10 TURN V -DIGITAL VOLTMETER 0

OHE INCH DISPLACEMENT CAUSES 0.050 VOLTAGE CHANGE Fig. 4-10 Electrical Displacement Transducer.

walls would not damage them.

However, reading the gages (through a telescope) proved to be slow and difficult, and, because the

. large deflections of the panels exceeded the 3" travel, the use

., of dial gages was abandoned.

A third method of measurement used a steel wire tension line

, from the

wall, wrapped around a

capstan pulley (Fig. 4-10)

. mounted on the shaft of a

ten-turn precision potentiometer

, (1000 ohm), in order to measure over a large range

(~SO") with a resolution of 0.02 in.

Accuracy of the method was bench-checked using a steel rule graduated in hundredths of an inch.

Over a

range of 2 ft, the measurements were found to be accurate and repeatable.

In use, electrical leads from the 11 electric dis-placement transducers were taken from the reference pylon where

. these units replaced the dial gages to a switch box and digital voltmeter measuring to 0.001 volt.

Thus, the deflection of all stations could be quickly and conveniently read at the same loca-

,tion where air pressure was controlled.

The electric transducers became the prime source of measure-

ment, but transit readings were made in all cases to provide backup measurements.

In two cases the electric units were not used because space limitations prevented use of the reference pylon.

Displacement measurements, along with time and temperature, were recorded at set intervals during both loading and unloading.

4.9 LOAD CONTROL Although an attempt was made to use displacement control in loading the

walls, load control was used in most cases (Fig. 4-11).

E,oading increments became smaller as maximum load was approached.

4-10

Monotonic loads were applied, and the displacements read as rapidly as possible.

This process was repeated up to maximum value.

Loading was stopped when it was judged that failure might be near.

In two cases (both 6" concrete block walls),

compres-sive failures did occur with complete rupture of the walls, but the safety cables prevented the walls from falling.

The rupture occurred only after the steel yielded and the walls deflected 17.7 in.

and 15.9 in., respectively.

The last wall, the 4" clay

-block wall, 16'igh, was intentionally carried to failure with

'a deflection of 17 in.,

which again occurred as a compressive failure but after the steel yielded and went into strain harden-ing condition.

In some -of the initial tests, several walls were partially

loaded, the bag deflated, and later the load was carried on up to l=

~ '0 00 50 40 30 x

20 I

10 6

00 50 40 30 0.7 psf/min, 0

0 D

0 0

0 o

0 0

0 0

d 0

OOd 0

do 0

0 0 od Oo d

d 0d 0

d od 0 d o Wall f/ 10 d Wall iI ll a Wall // 12 1.6 psf/min.

p 10 20 30 4p 50 60 70 80 90 100 110 120 130 140 150 160 170 Pressure in Air Bag psf Fig.

4-11 Rate of Latera'1 Loading; 9.6"-Thick Brick Walls.

4-11

maximum.

In most cases, displacement measurements were not made during unloa'ding.

A vacuum cleaner was used to assist in.

deflation.

4.10 TESTING ROUTINE After the testing routine had become well established, the time from beginning of inflation to maximum load was about 2 hr.

Initially, many problems were encountered in moving the test frame to a

new wall and rigging for testing.

At the end, it was possible to move the

frame, assemble it to the panel, and test one wall per day.

On one occasion, two walls were tested on the same day.

A crew of three or

four, along with the project director, participated in all tests.

4-12

SECTION 5 TEST RESULTS The test results for the 30 panels are presented here as plots of the load vs. deflection for each panel.

The deflection was measured for the mid-height of each wall.

A tabulation of I

the test results is given in Table 5-1:

materials, compressive

strength, vertical load, lateral load and lateral deflection at

) yield, maximum lateral deflection, and the date tested.

The maximum lateral 1oads shown ia the load deflection test, result curves (Figs.

5-2 through 5-9, 5-11, and 5-12) are those recorded in the test load readings.

They do not reflect correc-tion for loss of contact of air bag with the test panel when deflections exceeded 7 to 8 in.

(see Sec.

6.3 and the correction load deflection plot for Panel 24, Fig. 5-10).

The concrete tilt-up panels were reinforced with four 44 Grade 60 bars, and the masonry panels used five 54 Grade 60 bars.

Crack patterns for the panels can be seen in Figures 6-8 and 6-9 in the next chapter.

5. 1 CONCRETE MASONRY PANELS Of the nine concrete masonry panels, there were three panels for each nominal thickness:

10", 8",

and 6".

The actual thick-nesses were 9-5/8", 7-5/8",,and 5-5/8".

Three load deflection curves for each thickness are plotted on a

single chart (Figs.

5-2, 5-3, and 5-4).

It was fairly evident when cracking developed, as the slope changed significantly.

When the yield was reached, 'he slope shifted again, although this is less discernible on the charts.

5-1

TABLE 5-1.

SLENDER WALLS TEST RESULTS 1

Wall No. and Type 1

2 3

CMU 5

6 Thick-

ness, in.

9.63 9.63 9.63 7.63 7.63 7.63 5.63 5.63 5.63 f'r psl 2460 2460 2460 2595 2595 2595 3185 3185 3185 h/t Ratio 30 30 30 38 38 38 51.2 51.2 51.2 Vert.

Load, plf 320 860 860 860 860 320 320 320 320 Lat.

Load at f psfY 94 82 73 75 75 71 46 38 46 Defi.

at

Yield, in.

5.5 5.5 6.3 6.5 7.5 5.8

~ 9.0 9.8 Max.

Lat.

Defi.,

in.

17.1 8.0 3.9. 0 11.2 10.3 14.8 17.7 15.9 11.0 Date Tested 3-9-81 2-25-81 2-18-81 3-10-81 3-12-81 4-21-81 4-22-81 4-30-81 5-1-81 Br 10 11 12

,13 14 15 9.6 9.6 9.6 7.50 7.50 7.50 3060 3060 3060 3440 3440 3440 30.3 30.3 30.3 38.4 38.4 38.4 320 320 320

.320 320 320 94 89 74 40 54 66 9.3 9.0 12.0 14.0 10.5 15.6 16.8 14.6 19.6 15.9 14.8 4-20-81 4-17-81 5-11-81 5-8-81 5-7-81 5-6-81 16 HBr.

17 18 19 20 21 5.50 5.50 5.50 9.50 9.50 9.50 6243 6243 6243 4000 4000 4000 52.4 52.4 52.4 30.3 30.3 30.3 320 320 320 320 320 320 57 48 55 87 83 83 8.0 8.2 7.9 7.3 5.3 7.5 19 '

18.2 11.1 9.9 7.0 12.3 4-15-81 4-16-81 5-4-81 5-14-81 5-12-81 4-27-81 Con 22 23 24 25 26 27 28 29 30 7.25 7.25 7.25 5.75 5.75 5.75 4.75 4.75 4.75 4000 4000 4000 4000 4000 4000 4000 4000 4000 39.7 39.7 39.7 52.4 52.4 52.4 60.6 60.6 60.6 320 320 860 860 860 320 320 320 320 57 52 57 51 42 42 32 34 34 5.4 7.4 7.6 8.1 7.2 8.5 11.6 12.6 13.1

12. 2 11.8 11.8 13.2 11.1 12.4

13. 0 19.2 15.2 4-28-81 4-29-81 4-14-81 3-14-81 3-18-81 3-23-81 5-5-81 5-15-81 5-14-81 Note:

CMU = Concrete Masonry Unit; Br = Two-Wythe Brick HBr = Hollow Brick;

'Con = Concrete 5-2

Cracks for the masonry walls were essentially in the mortar joints (Fig. 6-9);

upon unloading, these cracks tended to close.

Depending upon the extent to which the wall was stressed beyond

yield, rebound was approximately two-thirds of the total deflection.

5.2 CLAY BRICK I

There were two thicknesses of clay brick masonry tested:

9.6" and 7.5".

These were of normal two-wythe grouted brick construction.

For each thickness, the curves were plotted on the load deflection diagram (Figs.

5-5 and 5-6).

Cracking occurred at the mortar joints,

,and because the mortar joints were relatively close to each

other, a uniformly

"'mooth deflection curve resulted.

Again, upon unloading, these

, cracks tended to close.

I 5.3 CLAY BLOCK MASONRY The three 5-1/2" clay block masonry panels exhibited normal

deflection characteristics (Fig. 5-7).

Two of the panels were

~ loaded to deflections beyond 18 in.

5.4 CONCRETE TILT-UP WALLS Four thicknesses of concrete walls were tested:

9-1/2",

7-1/4", 5-3/4",

and 4-3/4".

Three test specimens for each thick-

'ess are plotted on the load deflection charts (Figs.

5-8, 5-9, 5-11, and 5-12).

Deflection characteristics of the concrete tilt-up walls were similar to those seen in the charts for the other panel constructions, with a

sharp break at the cracking moment and then a change in slope at the yield moment where they flatten out.

0 5-3

The crack pattern was quite pronounced on the tilt-up concrete walls (Fig. 6-8), with cracks first developing at the center and

then, with increased deflection, the cracks were propagated further.

At maximum deflection, cracks were spaced apart approximately two times the thickness of the panel.

Upon

rebound, the cracks closed up somewhat but still were very much in evidence.

I' e

3 l 5 Fig. 5-1 'ypical Test Panel.

(This 10"CNU Wall Deflected 18".)

5-4

78

'O C$0 PANE 8 8 1

2 3

4 S

6 7

B 9

18 11 12 13 14 15 16 17 18 19

~-

Deflection in.

Fig. 5-2 Load Deflection Curves, 10" Concrete Block Masonry I

118

'..88 68

'; 58 mII 48 0

PANEL 8 PANEL 8 8

1 2

3 4

.5 6

7 B

9 18 11 12 13 14 15 Deflection in.

Fig. 5-3 Load - Deflection Curves, 8" Concrete Block Masonry 5-5

38 o~28 18 PANEL 8 7

PANEL 4 8

PANEL 8 9

8 1

2 3

4 5

6 7

8 9

18 ll IZ 13 14 8

Deflection in.

Fig. 5-4 Load Deflection Curves, 6" Concrete Block.'masonry

" 178 ls 16 17 18 "158 148 238 128 118 188 98 88 o

78 68 P NEL 8 11 8

1 2

3 4

5 6

7 8

9 18 11 12 13 14 Deflection in.

Fig 5-5 Load Deflection Curves, 9.6" two-Wythe Brick Nasonry 5-6 15 16 17

88

'- 58 48 38 PA EL ¹ 1

. PA EL ¹ 1

8 1

2 3

4 5

6 7

8 9

18 ll 12 13 14 1S 16 17 18 19 28 Deflection in.

Fig. 5-6 Load Deflection Curves, 7.5" two-Wythe Brick Masonry 78

""'8 48 o'8 18 PA

. PA EL ¹ 1

EL ¹ 1

0 8

1 2

3 4

5 6

7 8

9 18 11 12 13 14 15 16 17 1B 19 28 Deflection in.

Fig. 5-7 Load Deflection Curves, 5.5" Hollow Brick 5-7

o 38 PANEL 8 28 PANL 821 78 8

2 3

4 5

6 7

8 9

18 11 De flee tion in.

Fig.

5-8 Load - Deflection Curves, 9.50" Concrete Tilt-Up 12 13e 38 28 PAN I 8 22 PAN L 0 23 PAN L 8 24 8

1 2

3 4

5 6

7 8

9 18 De flee tion in.

Fig.

5-9 Load - Deflection Curves, 7.25" Concrete Tilt-Up 11 12 13

80 60 40 0

Relo~

3/24/81 Wall 24, 7.25" concrete Loaded 3/24/81 ded 4/

/8 4/14/81 Ind ica ted Loads

~ Loads Corrected for I

I Bag Contact Area 0

0 8

10 Deflection 12 14 16 18 Pig.

5-10 Load-Deflection Plot Corrected for Loss of Air Bag Contact in Mid-Span Area.

5-9

-+

28 ANEL 0 2S ANEL;8 26 ANEL 8 27 48 1

2 3

4 5

6 7

8 9

18 11 Deflection in.

Fig.

5-11 Load - Deflection Curves, 5.75" Concrete Tilt-Up 12 13 14 38 18 PANEL PANEL PANEL 8 28 8 29 8 38 8

1 2

3 4

S 6

7 8

9 18 11 12 13 14 1S 16 17 18 19 28 21 Deflection in.

Fig. 5-12 Load - Deflection Curves, 4.75" Concrete Tilt-Up 5-10

SECTION 6

INTERPRETATION OF TEST RESULTS 6.1 GENERAL PERFORMANCE Test results indicated general good performance of the wall panels in the range of the applied loads.

Elastic or inelastic lateral instability was not noted during the tests.

Wall panels continued to support additional lateral loading well beyond the deflection at which steel reached yield.

Interpretation of various aspects of results is given in the following subsections.

6.2 LOAD-DEFLECTION CURVES Typical idealized composite stress/strain relations for a

reinforced panel are shown in Figure 6-1.

A similar idealized relation holds for masonry except that the modulus of rupture (point 2) is considerably lower.

The load deflection results as seen in Figures 6-2 to 6-5 indicate that walls with h/t ranging

,- between 30 and 60 can resist 50% to 90% of their weight later-ally.

In addition, the lateral resistance is increasing even when deflections are extremely large.

This could be due to strain hardening of the reinforcing steel The load-deflection average curves were plotted for each panel thickness, and the results are discussed below for all four

, types of walls tested.

Concrete.

The average curves for concrete panels are given in Figure 6-2.

The near vertical incline reflects the panel stiffness when the panel performs as an uncracked section.

Panel yielding occurred at a deflection of approximately 3 in. for the 9-1/2"

panels, 5 in.

for the 7-1/4"

panel, 7-1/2 in. for the 5-3/4" panels, and 8-1/2 in. for the 4-3/4" panels.

6-1

YIELDING OF STEEL

'RACKIHG OF COHCRETE TENSILE YIELDING OF REINFORCING STEEL Eg CONPOSITE BEHAVIOR oF STEEL AND CONCRETE (SLOPE DEPENDS ON ANOUNT OF REINFORCIHG STEEL)

STIFFNESS OF CONCRETE STRAIN Fig.

6-1 Idealized Composite Stress-Strain Relations for Panel.

g8 tH.

Panels 19, 20, 21 (gI c8 0) 48

&8 O

Panels 22, 23, 24 Panels 25, 26, 27 anels 28, 29, P

30 For h/t values, see Table 5-1 8

1 2

3 4

S 8

7 8

8 18 11 12 13 14 1S 18 17 18 DEFLECTION IN in.

F~

6-2 Deflection in inches at Hid-Height: Concrete Panels.

6-2

e The onset of cracking (modulus of rupture) for all four thicknesses of concrete panels occurred at a deflection less than 1/2 in.

The cracking load increased with increase in panel thickness.

However, since all'the panels had the same reinforce-

ment, the percentage of reinforcement decreased with the increase in panel thickness.

As a result, the thinner panels with higher percentage of reinforcement had a higher percent of increase in load capacity from cracking to yield (compared to the thicker

, panels).

The cracking load for the 9-1/2" panel was approximately 90%

..of Ne yield capacity of the

panel, that is, Ne mcrease in capacity between cracking and yielding was only 10% of the total

~ yield capacity of the panel.

For the 7-1/4" and 5-3/4" panels the increase from 'cracking to yield was 30%,

while for the 4 3/4" panel the increase was 40%.

So it is seen that, in essence, the relative percentage of

,. steel reinforcement is the controlling factor in overall panel performance.

Concrete Block.

The average load deflection curves for the three different thicknesses of concrete block walls are shown in Figure 6-3.

The performance is similar to that of concrete panels except that the modulus of rupture was considerably lower.

The panels,

however, continued to sustain

load, and yielded at a

'oad considerably higher than the cracking load.

For the concrete masonry walls of 10, 8,

and 6 in., the steel reached the calculated yield stress of 70 ksi at deflections of 5,

.6, and 10 in.,

respectively.

Cracked performance started at approxi-mately 50%,

35%,

20% of the yield, respectively.

6-3

118 Panels 1,

2; 3

~ 78 68 Panels 4, 5, 6

,'58 48 Panels 7, 8, 9

For h/t values, see Table 5-1 8

1 2

3 4

5 6

7 9

9 18 11 12 13 14 15 16 17 16 Deflection in.

Fig

. 6-3 Def lee tion at 'Aid-Height:

Block masonry 6", 8", 10" Concrete 158 118 98 w 68

o. 78

'O o

Panels 10, 11, 12 9e~

Panels 13, 14, 15 For h/t values, see Table 5-1 8

1 2

3 4

5 6

7 9

9 18 11 12 13 14 15 16 17 19 19 Deflection in.

Fig. 6-4 Deflection at Mid-Height:

7.5" and 9.6" Brick 'Masonry 6-4

k.*hp f fkh." d." lyh'k panels (Fig. 6-4) was somewhat similar to that of the concrete block panels.

The rupture of the panels occurred at an early

stage, but the panels continued to sustain load.

For the 9.6" clay brick, the yield load was considerably higher than the rupture load.

The rupture load was approximately 40% of the yield load.

Yield is considered to have occurred at deflections of approximately 6 in. for the 9.6" thick wall.

The 7.5" thick wall demonstrated a low yield, with rupture approximately 60% of the yield load.

Yield for the 7.5" thick wall occurred at approximately a

7 in. deflection.

~11k.*hp f fkh." lyhl kp l

(Fig. 6-5) most nearly resembled the performance of the concrete block panels.

The similar configurations of the units is respon-

,~: sible for this, i.e.,

the cross-webbings of each type of block.

For the clay block panels, the rupture occurred early but the panels continued to sustain load.

The rupture load was approxi-mately 40% of the yield load.

Yield occurred at approximately 8-1/2 in. for the clay block panels.

6.3 AIR BAG CONTACT AREA There was a concern that a loss of contact area between the air bag and some side areas of the tested wall panel might have an effect on the test results.

However, calculations have shown that loads below yield remained unaffected and loads near yield weie only slightly affected.

The question arose when the notes for wall panel 17 showed a

6-3/4 in.

separation between the plywood frame and the tested

wall, whereas for wall panel 21 the notes show a separation of

~ about 3 in.

This was because the air bag was hung from the steel tubes in the former case and from the ledger angle in the latter 6-5

158 148 <

138 118 128 <

sa Ba Panels 16, 17, 18 e 518.

38 I~

L 28 18 J

J For h/t values, see Table 5-1 8

1 2

3 4

5 6

7 6

9 18 11 12 13 14 15 16 17 16 19 Deflection in.

'ig. 6-5 Deflection in Inches at Hid-Height:

5.5" Hollow Brick Hasonry.

Z oC Cl X

WO0o OI Uo Ulo<

~ i.

r.i On

~

OP 0

EO i.L CO<

4O BAG AS MANUFACTURED PERIMETER ~ 2X(18+48) ~ 132 IN.

10 0

CO VJ CO I

5 OC0 I

g) I I

C INFLATED BAG RESTRAINED BY WALL AND BACKING CA(132-rtXB)/2 UNCORRECTED~

o VERTICAL SECTION DEFLECTED WALL AND BACKING CORRECTED FOR LOSS OF CONTACT 5

DEFLECTION - IN.

Fig. 6-6 Bag Contact Area.

6-6

case.

From this time on, the floor positions were marked and the space between wall and plywood was consistently near the 3-in.

mark.

Figure 6-6 shows the method used to calculate a correction factor for wall panels 7,

13, and 29.

Data from the diagram of contact area was used to calculate the resulting bending moment.

From this, the pressure necessary to produce equal moment at midspan for uniform load was calculated to 44.0 psf. 'he corrected moment and the moment for this uniform load were then compared for each Zoot of height of the panel.

The average ratio of uniform load moment to corrected

moment, was 0.96;

hence, the effects of this discrepancy proved negligible.

6.4 CRACKING PATTERN Investigations of crack spacing in reinforced concrete

.members have indicated that crack spacing decreases with increas-ing applied load.

After stress reaches its critical value, the spacing of visible cracks remains approximately constant.

For

~ the average minimum crack spacing, t

< crack spacing

< 2t, where t is the thickness of the concrete cover (Broms, 1965).

Typical cracking patterns for concrete til<-up panels and for block walls are shown in Figures 6-8 and 6-9, respectively.

.For the block walls, the cracking occurred through bedjoint at the mortar block interface on the side opposite from the head joint.

These cracks propagated to approximately 3/4 of the thickness toward the compression side.

6-7

Fig. 6-7 Loss of Edge Contact of Air Bag with Wall Panel at the Middle Third.

6-8

Fig. 6-8 Typical Crack Pattern in Tilt-Up Wall After Major Deflection.

g l

Ht Cj t~ )

4 ~

Fig. 6-9 Typical Crack Pattern in Concrete Masonry Walls Under Large Deflection.

6-9

6.5 REBOUND C

j Unloading and reloading were carried out on concrete panel Nos.

24 and 27, with thicknesses of 7-1/4" and 5-3/4" respec-tively.

As shown in Figure 6-10, Panel 24 was loaded to a total midspan deflection of 13 in.,

which was 6 in.

beyond the point where the reinforcing steel reached the yield stress of 70 ksi.

Pressure was released and a

rebound of approximately 6 in.

was recorded.

The wall had a permanent set of 6-3/4 in.

Twenty days later the wall was again loaded, and its deflection path was just a little steeper than the first rebound curve until yield level was

reached, at which time a

shallower load deflection curve occurred until a total deflection of 18 in.

was reached.

The lateral load was then

released, and the wall again rebounded 6 in.

When compared with Panel 27 in Figure 6-11, it seems that the twenty day wait resulted in the stiffening of the panel.

Panel 27 was loaded to 43 lb and a deflection of 9 in.

This was just beyond where the calculated steel stress reached the yield level.

The load was removed and rebound readings taken.

The wall rebounded 5 in., to a permanent set of 4 in. even though the steel had just reached yield at mid-height of the panel.

If this panel experienced a near yield level loading, a

4 in. set would be expected afterwards.

Two hours later the panel was reloaded to a lateral load of 40 psf, unloaded to 20 psf, and then brought up again to the yield level.

When the wall reached the yield level it increased its rate of deflection until a total deflection of 16 in.

was reached at a lateral load of 45 psf.

This panel showed a

softening effect due to rebound and reloading.

The reloading appears to occur on a

slope close to the unloading slope.

In

addition, the area under the loading-unloading curve provides an indication of the nonlinear hysteretic damping of the 'system.

This data can be interpolated 6-10

70 60 v) 50 A

40 30 20 10 tested 3/24/81 tested -4/14/81 Panel 24, 7-1/4" concrete Versica1 Road 860 plf 2

4 6

8 10 12 14 16 18 LATERAL DEFLECTION IN in.

Fig.

6-10 Lateral Deflection at Mid-Height (Inches).

50 tested 3/20/81 c

30 20 10 Panel 27, 5-3/4" concrete Vertical load

= 320 plf tested 3/23/81 2

4 6

8 10 12 14 16 18 LATERAL DEFLECTION IN in.

Fig. 6-11 Lateral Deflection at Mid-Height (Inches).

6-11

to provide preliminary values to be used in the study of the dynamic performance of such panels.

6.6 SECONDARY MOMENTS DUE TO DEFLECTIONS P6 EFFECT Evaluation of effects of Ph moments is of primary interest in this program.

The ratio of the P6 moment when compared to the moment caused by vertical and lateral load is a good indi-cator of this secondary effect.

The procedure used for finding the Ph moment at the mid-height of the panel is given by Pb, Moment

=

Roof Load x 6 + Wall Weight Above x b,

(6-1) where Pb, moment Roof load Additional moment at the midheight due to deflection, lb-ft Vertical load per foot acting on the ledger angle (320 lb and 860 lb/ft were used in the the present tests)

Midheight deflection, ft Wall weight above Weight of the wall above the midheight, lb/ft The percentage of Pb, moment can be found from the expression

/ Pb, Moment

=

Ph Moment x 100 w h P

~

e

+

8 2

6-12

where Pb, Moment

=

% ratio of Ph moment to the applied moment-w

=

Applied lateral load, psf; Panel height (24 ft)

Roof load/ft (320 lb/ft or 860 lb/ft)

Roof load eccentricity, ft (e

= 0.25 ft +

1/2 x panel thickness in ft)

The percentage of Pd, moment found from Equation 6-2 is plotted versus normalized deflg.ction in Figures 6-12 through 6-14.

The deflection plotted on the abscissca has been divided

'by the height of the panel.

In a normal wall design the hori-zontal deflection to height ratio is usually less than 0.005.

It

,never exceeds 0.01.

The Ph plots in the above figures show that

,when deflection to height ratio is less than 0.01, the percentage of Ph moment is less than,15%, i.e.,

73 for b/h

< 0.01

% Pb Moment 15%

(6-3 )

53 il L

C I

E43~

K 4 38 r

~e L

18 l-L I

2 3

5 (Deflection/Height)

X 100 Fig

~

6-12

% Ph Moment, 4.75" Concrete Tilt-up 6-13

is <

2 3

4 (Deflection/Height)

X 100 Fig. 6-13 Pb,

Moment, 6" Concrete Block

{

6 M

l

<l o<4 23 I

I 3

3 2

3 (Deflection/Height)

X 100 Fkg. 6-14 X PD Moment, 5.5" Hollow Brick 6-14

e This significant result shows that, in the normal working ranges of design, the Pb, moment is a minority contributor to the total moment.

6. 7 AXIAL FORCE-MOMENT INTERACTION DIAGRAMS The axial force-moment interaction diagram serves as an indicator of the strength of the cross sections.

When the actual material properties are used in the Whitney stress block proce-

dure, an accurate representation of the strength is obtained.

Interaction diagrams of several configurations are shown in Fig-ure 6-15.

The axial load, P

strength of the 5.5" clay brick panel is larger than thicker concrete and concrete block panels because of the high f'alue for the brick.

0 1588 IM8 1288 1188 1888 888 0

688 788 688 588 X

5.5 IH %1CK

~ ~7.25 IH COCKIE

~8IH CtKRETE ROCK

~ 4.75 IN CCCKIE L) ~

r S

18 1S 28 25 38 35 48 4S 58 SS 68 65 78 75 88 BS Moment ft-kips Fig.

6-15 Interaction Diagrams of Four Configurations.

6-15

In the present

tests, our interest in the interaction diagrams lies in the low axial load range.

A representation of the interaction diagrams for the low axial loads i" given in Figure 6-16.

In this range the moment strength increases slightly with axial load.

The moment strength is primarily dependent on the amount and depth of steel in the cross section.

g4 7

8 0

5 4

X 3

r r

r

~/

y I/

I 8/

l 18 15

.foment ft-kips Fig. 6-16 Interaction Diagrams at Low Levels of Axial Load.

The resisting moments and axial forces in two concrete and two block panels for various deflection to height ratios are plotted in Figures 6-17 and 6-18.

Figure 6-17 is a plot of axial load or force versus moment.

The two almost: vertical lines representing predicted strength of 4.75" and 9.5" thick concrete panels were found from the inter-

'ction diagram calculation procedure.

Actual f' 4 ksi and c

6-16

f

= 70 ksi values were used in the calculation.

The points y

clustered around each curve are the measured moments and-axial forces in the panel for various deflection to height ratios (b/h).

For the thin 4.75" (h/t = 60) panel the measured moment corresponding to b/h = 0.005 is approximately 60% of the pre-

. dicted yield moment.

In the case of a thicker 9.5" (h/t = 30) panel the measured moment corresponding to b/h = 0.005 is 95% of the predicted yield moment.

This result shows that for thin

panels, deflection constraints will control the design while for thick panels, strength will be the limiting constraint.

The measured moment exceeds the predicted moment for 6/h

> 0.02 in both panels (Fig. 6-17).

This occurs because of strain hardening of the reinforcement.

A similar plot of measured moments for various b,/h values is plotted on an interaction diagram representing block panels in Figure 6-18.

Here the measured moments do not exceed the pre-dicted yield moment in the 6" block panel.

A similar result is found for the 10" panel except when b/h = 0.03.

The'block panels are more flexible

. than the concrete panels and therefore reach

"" larger deflections 'before yield occurs.

Deflection would be an important consideration in design of both 6" and 10" walls.'hese figures show an expanded scale of the portion of the interaction curve located near the origin.

The points plotted on the large scale curve are the yield point moments determined by test.

The variation between the test moments and the predictive C interaction

curves, for the most part, have been attributed to the mislocation of the reinforcement.

Good agreement was obtaind for concrete, concrete

masonry, and the brick panels.

6-17

18 9

7 Ql 6

Interaction curves LA rm lSl tel

+

+

+

6/h values 5

0 4

~d/h values Moment, ft-kips Pig.

6-17 Neasured ifoments for Various 6/h Levels Compared with Interaction Diagrams for Concrete Panels.

I/h values iA 6

"5 c50 4

X 2

CA (57 I%I CSI 5/h values Interaction curves

.'foment, ft-kips

Fig, 6-18

'measured Moments for Various 6/h Levels Compared with Interaction Diagrams for Concrete Block.

6-18

6.8 PREDICTIONS OF DEFLECTIONS USING MOMENT CURVATURE RELATIONSHIPS The fundamental theory for flexural deflection is based on a relationship of moment and curvature.

Accordingly, a mathemati-cal model was constructed for computer analysis to compare results with the experimental data.

The method must first develop the interaction curve based on the section properties.

The interaction diagram uses the Whitney stress block concept, and the depth to the neutral axis is the basis for computing the curvatures corresponding to the load and moment points.

From the interaction

diagram, a

family of Moment/Curvature relationships for each point on the wall is generated since the vertical load varies with height of the wall.

After obtaining the Moment/Curvature relationships, a moment based on wl /8

+ Pe is applied and a set of curvatures is

obtained, which are then integrated,.to obtain an initial set of

.deflections that are used to calculate the Ph moments, which are added to the original

moments, and a

new set of curvatures are generated and integrated.

This continues until the solution converges.

Application of this procedure to the test walls produced load/deflection curves that had excellent correlation with the test results.

The results for the 9.5" concrete panel are shown in Figure 6-19.

39 I~Test result Predicted I

i l

18 5

ll~

S 2

Deflection, inches

'ig. 6-19 Predicted and Test Curves for 9.5" Concrete Panel.

6-20

SECTION 7 DEVELOPMENT OF DESIGN METHODS

7.1 INTRODUCTION

The experimental results demonstrated that wall response to horizontal loads resembled the behavior of shallow reinforced concrete beams subjected to uniform load (Ref. 13).

After

cracking, the walls were flexible, and after yield their load-deflection curves were flat.

Shear failure or bond slip did not

occur, so that even when deflections were large, a reduction in panel resistance did not occur.

Vertical loads used in the experiments were chosen to repre-sent typical tributary design loads used for buildings in

'California.

Panelized wood roof systems used in single-story construction generate loads that seldom exceed 300 lb/ft.

The gravitational weight per unit length of tilt-up and masonry

.panels is much greater than the tributary roof load per unit length.

The vertical load at the foundation level is usually four to eight times greater than the roof load.

Therefore, any secondary moment (Ref. 25) in the panel due to vertical load will be primarily caused by the weight of the panel.

The roof load will contribute only 12 to 25% to the secondary moment.

During the experiment, the lateral pressure load imparted to the panel by the air bag was increased until deflections reached two to three times the panel thickness.

Up to the yield level, the relationship between lateral load and midheight lateral deflection resembled a bilinear

form, which means the response can be represented by two straight lines (Ref. 28).

The charac-teristics of the bilinear relationship are shown in Figure 7-1.

Up to a load that induces

cracking, the response is described by a steep, straight, line.

During a further load increase, a crack-ing pattern is developed and the load deflection relation is 7-1

curved.

After the cracking pattern has stabilized, further increases in the load induce a low-slope, straight-line response.

Mathematical representation of load-deflection relations, such as those depicted in Figure 7-1, go back to the 1940's.

Accurate predictions can be obtained using methods similar to

those given in Reference 41.

Even the curved portion of the

-. load-deflection curve can be predicted easily (see Sec.

7-6).

The testing and analysis work of the Slender Walls Test Program focused heavily on design considerations.

The analysis methods developed herein are intended for use in design.

Load-deflection relations are needed because both strength and serviceability are considered in slender wall design.

Yield Deflection e

Fr cra kea Cracked Sect ion; Cracking Pattern is Stabilized

Cracking Deflection Developtkent of Cracks due to Loading C5 kao aa No Cracks Induced by Load

~ Kl Cross A

Fy cg CJ No Cracks Induced by Load Nidheighr. Horirontal Deflection, I'.

Fig. 7-1 Characteristics of Bilinear Load-Deflection Relation 7-2

0 7.2 DESIGN VARIABLES The principal design variables are wall height, thickness, and amount of vertical reinforcement.

The height dimension is set to satisfy functional and architectural needs.

Under the current code procedures, wall thickness is then chosen to satisfy the height-to-thickness ratio (h/t) requirements (Refs.

1, 14, 38).

Strength requirements are considered when selecting amounts of reinforcement.

Frequently the minimum percentages are used in order to satisfy temperature and shrinkage requirements.

The measured flexibility of the wall specimens showed that some of the thin walls with high h/t values resisted the factored

,.design loads without yielding, although the deflections were large (Fig. 7-2).

7.3 STRENGTH AND DEFLECTION CHARACTERISTICS The 6"

concrete block panels that were tested had an

" h/t ='51.2.

The reinforcement ratio based on the gross section, p,

was

0. 0037.

These panels exhibited significant horizontal gdeflections under service loads and yet carried loads in excess

'f the factored design loads without yielding.

A load-deflection curve representing the average of the three panel responses, shown in Figure 7-3, will be used to present strength and stiff-ness characteristics.

The midheight deflection of the panel was 2.5 in.

when it was subjected to a lateral service load equal to 17.4 psf, or 30%

of the wall weight.

When this deflection is converted to a

height/horizontal deflection

ratio, h/d

= 24 x 12/2.5

= 115.2.

The height/horizontal deflection ratio is similar to the span/

vertical deflection ratio used as a design criterion for limiting vertical deflections in beams (Refs.

1, 14, 38).

For horizontal beams a ratio of 115.2 indicates a large deflection;

however, a

ratio of 115.2 is an acceptable value for the walls of a one-story building.

7-3

Fig. 7-2 Flexible 6 in.

Concrete Masonry Panel L

'L

~

$ S

~'

L

('

~

S

~((

S 0

((0 30

') O AVERAGE LOAD-DEFLECTION RELATIRf, CFNFRATED FRO'I DATA IO 3

3 I(

S A

7 8

9 IO Il NIVIFICIT DEFLECTICII, IN.

Fig. 7-3 Load-Deflection, 6" Concrete Block Masonry.

0 7-4

e The measured load-deflection curve (Fig. 7-3) reached a

yield level when the lateral load was 41.2 psf.

This lateral load is equivalent to 71% of the wall weight.

The ratio of measured yield load/service

load, R

, is 2.36, which is a large value.

In ultimate strength design (Refs.

1, 14,

38) the ideal design yield load/service load ratio, R

, is given by R

1.75 U

1.4 4E 0.8 (7-1) where U = ultimate load,

= 0.8 (see Sec. 7.5),

and E = earth-quake service load.

Since the measured

ratio, R

exceeds the m'deal design ratio, R

(i.e.,

R R ), the ~panel can carry the m

factored loads without yielding.

,h For a panel design to be considered

adequate, the panel must meet both de flection standards and strength standards.

The 6"

concrete block panel with p

=

0.0037 carried the factored designs loads with margins to spare; its height/deflection (h/6) ratio was h/b,

=

115.2 when subjected to a

service load.

Therefore, the finding of the research project is that this panel barely meets deflection design standards when a reasonable h/b, limit (h/b,

=

100; see section 7.4.2) is used.

The panel easily satisfies the requirement for strength under factored loads.

7.4 STRENGTH AND DEFLECTION DESIGN CRITERIA The design criteria selected by the Committee are deflection under service load and yield strength under factored load.

A successful design must satisfy both criteria.

7.4. 1 STRENGTH CRITERIA Loads and resistance are considered when strength is evaluated.

7-5

Loads 1.

Factored loads are based on:

U

=

0.75 (1.4D

+ 1.7L + 1.87E) or U

=

0.75 (1.4D + 1.7L + 1.7W) or U

=

0.9D

+ 1.43E or U

=

0.9D + 1.3W (7-2) whichever is the most severe.

These load factors are used for design of elements,

systems, and connections of a building sub-jected to either seismic or wind forces (iSec.

2609, UBC,

1979, 1982 eds.).

Essentially they are used for out-of-plane forces

)

in the design of tall, slender walls.

Other load factors, where gs 1

U = 1.4 (D

+

L + E),.are for shear walls and frames that, at the discretion of the designer, are used to resist forces parallel to them (Sec. 2627(d),

UBC, 1979, 1982 eds.).

2.

Lateral and vertical loads are used in computing the maximum design

moment, M

, which, for practical purposes, occurs at the midheight of the panel.

3.

Secondary moments

- induced by deflections at the mid-height of the panel are included in the maximum design

moment, M

4.

Axial forces at midheight include effects from roof load and panel weight.

7-6

0 Resistance or Ca acit of Panel Cross Sections 1.

Ultimate strength design concepts are used when evalu-ating the moment. capacity of cross sections.

A Whitney stress block idealization is assumed for the compressive stress distri-bution in the concrete and the masonry (Ref. 18).

This rectangu-lar stress block is a simple generalized form of the ultimate stress strain curve when maximum strain of 0.003 'is achieved.

The design compressive strength, f', is used for concrete c

calculations.

Similarly, f'or masonry can be an assumed value or can be established from prism tests.

Yield stresses

.used iz reinforcement calculations correspond with the grade of the reinforcement.

The limiting compressive strain in the concrete masonry units and brick masonry units is an important consideration in Zultimate strength design.

In the present

study, a limiting compressive strain of 0.003 was used for both concrete and masonry materials.

The balanced reinforcement percentages, p>

and p b, found gb':using the tested values for f', f',

and f

are listed in Table 7-1.

Also included is the actual reinforcement percentage, p

that was used in the panels.

The actual reinforcement g

percentage/balanced reinforcement percentage ratio p /p b is g

gb also given.

7-7

TABIE 7-1

~

BALANCED REINFORCEMENT PERCENTAGES Tested Values, f

= 70, 000 psi y

6" CMU 8"

CMU 10" CMU Type f'r fI pSi 318S 2595 2460 0/

Balanced Pb*

1.82 1.48 1.41 0/

Gross Balanced P bt 0.91 0.74 0.71

/

Actual p

0.37 0.27 0.22 Ratio

'g Pub 0.41 0.36 0.31 5-1/2" Hollow Brick 6243 9-5/8" 2-Nythe Brick 3060 3.57 1.75 1.79 0.88 0.38 0.22 0.21 0.25 4-3/4" 5-3/4" 7-1/4" 9-1/2 Concrete 4000 Concrete 4000 Concrete 4000 Concrete 4000 2.29 2.29 2.29 2.29 1.15 1.15 1.15 1.15 0.35 0.29 0.23 0.18 0.31 0.25 0.20 0.15 Design Values, f

= 60,000 psi y

6" CMU 8"

CMU 10" CMU Type f I or f I pRi 1500 1500 1500 Balanced Pb*

1.07 1.07 1.07 Balanced Pgbt 0.54 0.54 0.54 Maximum Design p

0.32 0.32 0.32 Maximum PQPtIb 0.59 0.59 0.59 5-1/2" Hollow Brick 5-1/2" Hollow Brick 2500 5000 1.78 3.56 0.89 1.78 0.40 0.40 0.45 0.22 9-5/8" 2-Wythe Brick 1800 1.28

0. 64 0.40 0.63 4-3/4" 5-3/4 7-1/4" 9-1/2

'oncrete Concrte Concrete Concrete 3000 3000 3000 3000 2.14 2.14 2.14 2.14 1.07 1.07 1.07 1.07 0.53~

0.53 0.53 0.53 0.50~

0.50 0.50 0.50

• Percentage based on d

distance, i.e.,

d = t/2, based on Equation 7-3.

Percentage based on t (Eq. 7-4).

p

(

0 320/

g 0

5 0 50 p b (Eqs.

7-3, 7-4, and 7-5).

(Ref.

1, Appendix A).

7-8

The present code limitations on balanced steel for concrete flexural members is considered to be satisfactory for the preven-tion of brittle failure.

For the 6" concrete masonry panel, the block prisms had f'

(tested)

=

3185 psi, which is a high value for block with a

specified masonry assembly design strength f'design) 1500 psi.

A more realistic tested compressive strength of the

~ block is 2200 psi for Grade N units with a specified masonry assembly design strength f'design)

=

1500 psi.

The over-m strength of concrete masonry units is explained by reviewing the ASTM requirements for block properties.

The compressive strength of Grade N units must be at, least 1000 psi on the gross area for the average of three units.

To meet the ASTM C90 requirements of 1000 psi compressive strength based on the gross area, it is

. necessary to manufacture block with an average compressive strength of 2200 psi based on the net area.

The grout used in masonry assemblies with f'design)

=

1500 psi must have a

'8-day minimum strength of 2000 psi.

The average compressive strength of grout will exceed 2200 psi.

Therefore, the block.

will have at least the value f'tested)

= 2200. psi.

I References 14 and 38 state that an f' 1500 psi may be assumed without tests when the requirements of ASTM C90 for con-crete block Grade N and ASTM C62 or C216 for clay brick Grade MW with 2000 psi grout and'type M or S mortar are specified.

A balanced reinforcement percentage, pb, for f'design)

'1500 psi for concrete masonry units based on the more realistic strength of the block and f'tested)

=

2200 psi and f

m Y

(tested)

= 70,000 psi is m f 87,000 b

f i87,000

+ f y

y (7-3 )

7-9

where P

=

0. 85.

With d

= t/2, the balanced percentage of tension steel based on the gross cross-sectional area, p',

is gb' P b

=

2 Pb g

(7-4)

It was decided to limit the design p

to 1/2 of the g

in Equation 7-4; therefore, for concrete masonry p b given 1

Pg 2

Pgb 0.32% for f

=

60,000 psi 0.50% for f

=

40,000 psi (7-5 )

A p

(design)

~

0.32% is a conservative limit value for concrete masonry units with f'design)

=

1500 psi and f

m

,. (design)

= 60,000 psi.

In the tested 6" concrete masonry block

panels, the p

(tested)

= 0.37% but it was necessary to use p

g g

(design)

< 0.32% because of the high f'tested)

= 3185 psi found m

from the block prism tests.

e A listing of design p 's and ratios for f

= 60,000 psi g

is given in Table 7-1.

The p

values for concrete

block, g

brick, and concrete walls are listed.

The p

(design) values g

for hollow brick units and two-wythe brick units is limited by p

(design)

~

0.40%

for f'design)

=

1500 psi and fY (design)

= 60,000 psi.

This is conservative since the strength of brick units falls in the 5000 to 6000 psi range.

Flexural forces acting on over-reinforced cross sections may cause brittle failure.

The maximum design p

and maximum g

pgp b

values were set at low levels so that brittle failures can be avoided.

More testing is needed to establish the upper limit of the p /p b values.

gb 7-10

2.

Axial forces are considered when evaluating the moment

strength, M, at the midheight cross section.

A capacity,reduc-n'ion factor, ), is used in the relation M

5 g

M which required that the maximum design moment must be less than or equal to the moment capacity reduced by the

)

factor.

7.4.2 DEFLECTION CRITERIA Loads and stiffness are considered when deflection is evaluated.

An h/b, limit is selected, which keeps the midheight deflections within acceptable limits.

The purpose of the deflec-

'"tion computation is to prevent designs of overly flexible panels and to'ssure reasonable straightness after a

service level lloading Lateral Loadin 1.

Norking or service loads are used when calculating the midheight deflection.

2.

Lateral and vertical loads are used in computing the maximum horizontal deflection, which for practical purposes occurs at the midheight of the panel.

3.

Secondary moments induced by deflections at the mid-

"height of the panel are represented in the deflection calcu-lation.

4.

g factors are not used in the deflection calculation.

Stiffness of the Panel 1

~

The load-deflection relation for the panel is assumed to obey a bilinear law (Fig. 7-1).

7>>11

2.

The slopes of the straight line parts of the load-deflection curve are as follows:

(a) up to cracking

load, a

gross section I is used to compute deflection from the load; (b) additional deflection beyond the cracking.load is computed with the cracked I.

The ratio of gross to cracked moment of inertia varies between 10 and 25.

I values for panels used in typical designs are given in Table 7-2.

3.

The load at. which cracking occurs is observed from the experimental data.

The modulus of rupture and cracking moment can be computed from the cracking load.

4.

The midheight deflection, b, is computed for a panel with simple support at the top and bottom.

In this procedure,

. called the Ph Method, the 6

is found in the following:

SNh 48EI gross for N<

N 5

M h

5(M -

M

)h 48EI gross 48EI for M

<M<M cr yield where h

=

Height of the wall M

=

Service moment at the midheight of the

panel, including P-6 effects (see following section for midheight moments)

E

=

Code-prescribed modulus of elasticity of the concrete (Ref.

1) or masonry (Ref. 39)

I I

I 7-12 I

~

ross, cracked moment of inertia of the wall cross section cr'n Cracking, strength moment of the concrete or masonry 5.

The deflection at the top of the panel is assumed to be zero in Equation 7-6.

The effect of diaphragm deflections on midheight motions of the panel is not considered in the deflec-tion calculation.

This is not in conflict with the purpose of the deflection calculation, which is to eliminate overly flexible panels.

6.

The deflection Equation 7-7 is based on simple support.

conditions.

Deflection calculations for other top and bottom support conditions must be performed using more basic procedures such as moment-area or virtual work methods.

A "dock height" building is a case in which moment area or virtual work methods are needed.

Selection of h 6 Limit The midheight deflection found from Equation 7-6 is limited so that a serviceable panel is designed.

The deflection limit to be used in calculations is given by the relation h/6

= 100 The maximum deflections allowed are directly proportional to the height of the wall.

A tabulation of maximum deflections is given in Table 7-3.

These are large deflections, but they ar'e manage-able in industrial buildings.

Higher and lower values for the h/6 limit were considered.

A higher value would eliminate tall, slender walls with high p

values.

-A lower value would permit g

unserviceable panels with midheight deflections that are very large.

7-13

TABLE 7-2.

GROSS AND CRACKED MOMENTS OF INERTIA (I in.

)

OF TYPICAL PANELS PER FOOT OF WIDTH TYpe Gross I Gross I Cracked I Cracked I Cracked I Gross I

Cracked I, 4-3/4" Concrete 5-3/4" Concrete 7-1/4" Concrete 9-1/2" Concrete 107.2 190.2 381.1 857.4 p

= 0.20/

g 4.2 7.4 14.9 33.5 25.6 25.6 25.6 25.6 p

= 0.40/

7.3

12. 9 25.9 58.2 14.7 14.7 14.7 14.7 Note:

f' 3000 psi for concrete c

6" CMU 8"

CMU 10" CMU

~'177.1 443.3 891.7 p

= 0.20/

12.5 31.0 62.4 14.3 14.3 14.3 p

= 0.32/

17.3

43. 0 102.6 10.3 10.3 10.3 Note: f' 1500 psi for CMU Jll 5-1/2" Hollow brick with f'

2500 psi m

5-1/2" Hollow brick with f'

5000 psi m

166.4 166.4 p

= 0.20/

7.8 4

21.3 38.1 p

=

0.40%%u 13.4 7.8 12.5 21.3 9-5/8" Two-Wythe 884.7 Brick with f'

1800 psi m

53.8 16.4 89.9 9

8 7-14

TABLE 7>>3; MAXIMUMALLOWABLE DEFLECTIONS FOR WAZLS OF VARIOUS HEIGHTS BASED ON h/b, = 100 Wall Height, ft 15 20 25 30 35 Midheight Deflection, in.

1.8 2.4 3.0 3.6 4.2 t

The moment at the midheight of the wall can be found from statics.

Consider the panel support ~d free body diagrams shown in Figure 7-4.

The horizontal force at the roof line, H

, is found by summing moments about B.

The result is 2PE Pe weal ~

0 2

3h h

(7-~)

where P

P Horizontal force at the roof line Zateral load acting on the panel Weight of the panel Load at the roof line Eccentricity of the roof load 7-15

I I

I pA 0

TABLE 7-3.

MAXIICJM ALLOWABLE DEFLECTIONS FOR WALLS OF VARIOUS HEIGHTS BASED ON h/b, = 100 Wall Height, ft 15 20 25 30 35 Midheight Deflection, in.

1.8 2.4 3.0 3.6 4.2

7. 4. 3 DETERMINATION OF MOMENTS AT THE MIDHEIGHT OF THE PANEL The moment at the midheight.

of the wall can be found from statics.

Consider the panel support and free body diagrams shown in Figure 7-4.

The horizontal force at the roof line, H, is found by summing moments about B.

The result xs

2PB, Pe wh ~

0 2

3h h

where P

P Horizontal force at the roof line Lateral load acting on the panel Weight of the panel Load at the roof line Eccentricity of the roof load 7-15

Hp 3

pp/p Hidhei ht A'H~

B Fig. 7-4 Panel Support and Free Body Diagrams.

By summing moments about the panel midheight, the relation for midheight moment, M, is obtained:

h2 P

b, P

e M

=

+

+ P b, +

wh 8

2 o

2 The moment found from Equation 7-10 depends on the midheight deflection, d,.

The deflection 6

is found from Equation 7-7, where, it is noted, M

is required as input there; this is an l

iterative process.

It has been shown that Peh/2 and Ph were not the dominant terms of Equation 7-10 (Ref. 32).

Therefore, this iterative procedure using approximate values of M

and b,

will converge rapidly.

The approximation for the midheight moment in the i + 1 iteration cycle is found after Equation 7-10 is modified to 7-16

4p 30 AI 20 lo PA% L7 PANEL 8 PANEL 9 fr ~

3/f'r 2 ~f' 0

r g IM 0

CL 0

0.3~~

q S ~

0 0"

0 0

0 6

1 2

3 4

5 MIDNEICIlT DEFLECTION, IN.

Fig. 7-5 Selection of $ Factor and Cracking Moment: 6" Concrete Block Masonry.

mine M

and

)

values that put the

)w vs.

b, relations on the safe side of the experimental data.

The use of the

'"':factor for putting prediction relations on the safe side of

'xperimental data is a widely accepted approach (Ref. 15).,

For simplification of design, the number of different M

and

)

values was kept to a

minimum.

Different M

and values were used for each type of material, i.e., concrete, con-f crete block'asonry, hollow brick

masonry, and wythe brick

'asonry.

Each type had distinct force-deflection properties, and

'"thus different M

and

)

values were needed for accurate cr prediction of behavior.

The M

and

)

factors that were cr selected for the different, materials are 'as listed in Table 7-4.

For the

)w vs.

b, relations that incorporate these M

and

values, plots for three panel types are given in Figures 7-6 7-19

through 7-8.

The M

and p

values were cr the

)w vs.

b, plots for each type of through 7-8).

The values were selected so point fell below or near the lower boundary thicknesses of panels of the same type.

chosen by inspecting material (Figs.

7-6 the predicted yield of the data for all Values of M

and g

for masonry panels subjected to non-cr continuous inspection listed in Table 7-4 were selected so that, the wall heights for various thicknesses and reinforcement per-centages were essentially the same as allowed under present codes when the arbitrary h/t limit is not imposed.

Special Inspection Noncontinuous Inspection TABLE 7-4.

AND M

• FACTORS FOR DIFFERENT MATERIAL cr TYPES USED FOR WALLS Factor Concrete Concrete Masonry Units Hollow Brick Masonry 0.9 0.8 0.85 Two-Wythe Brick Construction 0.75 0.8$

Factor 0.72 0.64 0.68 0.60 fr*

5~f'.5jf

'.5Jf'.

O~f'M

=

Sf 7-20

50 0 Q 40 YIELD

~p Q

4 w vs.

6 Relation CI O

gg 0

30 Q

20 0

0 ~ 9 ~

fr = 5 '0 ~fc Mcr =

S f 0 PAklEL 22 0

PANEL 23 Q

PANEL 24 10 0.5 1.0 1.5 2.0 MIDHEIGHT DEFLECTION IV.

2.5 3.0 3.5 Fig. 7-6 M

and

$ 7. 25" Concrete Panel cr 40 2

PANF.L 7

0 PANEL 8

Q PAVEL 9

30 C

20 C

10 Q

Q& 0 4 w vs.

6 Relation 4 = 0.8, fr = 2.5 ~f>

Mcr S

YIEL 3

4 MIDHEICHT DEFLECTIOV, IN.

Fig. 7-7 M

and Q

6" Concrete Block Masonry cr 7-21

50 40 d PANEL 16 0

PANEL 17 O

PANEL 18 do 0

30 CI 20 4

10 Oo o

0 o

o 0

4> w vs.

6 Relation 085~

fr~ 2

~ 5 vfc Mcr =

S fr 0

0.5 1.5 2.5 3.5 4.5 NIDHEIGHT DEFLECTION, IN.

5.5 6.5 7.5 Fig. 7-8

$ Selection 5.5" Hollow Brick Masonry 7-22

0 SECTION 8 DESIGN KGQ1PLES

8.1 INTRODUCTION

Two design methods for walls of buildings with small axial loads have been formulated, and are presented here in the form of seven example problems.

Both methods incorporate modulus of rup-

ture,

)

factors, determination of d

at service loads and at factored ultimate loads; these elements ensure that designs fall on the safe side of the experimental data.

It is of primary importance that both serviceability and strength require-ments are satisfied in each method.

The serviceability requirement concerns deflection under service load; it is a

necessary condition that the midheight deflection of the wall does not exceed 1/100 of wall height.

The strength requirement is calculated using factored loads.

The factored moment, M

, includes both Pe and Ph moments that are u'dded to the primary moments due to lateral and vertical loads.

factors are used "to account for the variability of material performance, effects of tolerances, and reliability of the com-putation.

The

,nominal

moment, M

is found from ultimate n'trength theory.

The strength requirement is M

< fM u

=

n The proposed design methods are intended to replace the current code methods with their arbitrary h/t limitations (Refs.

14 and 38).

The proposed methods agree closely with measured load-deflection behavior that occurred during the experimental testing program.

Examples 1

and 2

use the Ph Design

Method, an iterative approach to determine de flections for calculating magnitude of secondary moments.

Examples 3

through 7

use the Yellow Book I"

8-1

Method to determine deflection at service load and at of steel in order to determine the secondary moments.

the examples from the Yellow Book Method are given in sheet format common to engineering practice.

the yield Note that the work-8.2 DESIGN EXAMPLES USING Pb, DESIGN METHOD Two design examples using the PA Design Method developed in this report are presented here in problem format.

EXAMPLE 1:

Given:

A 20'-tall hollow brick masonry constructed with 5.50" units.

The fully grouted wall is simply supported at

, the top and bottom.

The unit weight w = 56 psf and 5000 psi.

The f

= 60 ksi The wall is reinforced m

with 54 reinforcement.

The spacing, s, is 18 inches.

The roof load is 320 lb/ft applied through the ledger

.with a 3" eccentricity.

Required:

Determine if the wall is adequate.

Solution:

1.

Material Guantities a.

Modulus of Elasticity E

= 1000 f' 5 x 10 psi 6

m m

b.

Modular Ratio n =

E /E

= 29 x 10 /E

= 5.8 6

s m

m 2.

Geometric Quantities a.

Steel Ratio based on Gross Section p

= A /spacing x t = 0.2/18 x 5.5

= 0.002 g

S b.

Distance to Steel d

= t/2

= 5.5/2

= 2.75 in.

8-2

3.

Weights:

Based on b = 12 in.

a.

Superimposed Vertical Dead Load P

= 320 lb.

0 4,

b.

Weight of Wall w = 56 psf; lateral load

= 0.3 c.

Total Weight of Wall P

= 56 x 1 x 20

= 1120 lb/ft P

Deflection Calculation a.

Modulus of Rupture f

= 2.5 g f' 177 psi w = 0.3 x 56

= 16.8 psf b.

Section Modulus and Moment of Inertia Based on Gross Section S

= bt /6 = 60.5 in.

I

= bt

/12

= 166.38 in.

2 3

3 4

gross c.

Moment at Cracking M

= Sf

= 10,700 lb.in.

cr r

d.

Cracked Moment of Inertia N.A.

np bt:

8

'(d-kd) 0

= 2n p d

= 0.0638 g

f3 = 2n p d

0.1755 2

g kd = 0.5 u+

0

+ 48

= 0.3882 in.

2 Moment of Inertia of Cracked Section

=

+ np ht (d kdj

= 4.5047 i.n.

b kd 2

4 cr 3

g e.

Calculate Mid-Height Moment Under Service Load by Iteration Set

~

=

0 1

1 2

p P

e wh

+

P

+ p gl +

o (Eq. 7-11) 2 M2 0.3 x 56 x 8 x 12 11,000 lb.

2 Since M

240

~ 1120 x 0 + 320 x 0 + 320 x 5.75 2

in.

Mcr 5

cr M

h 48EI gross 5

(

cr)

M M

h 48EIcracked (Eq 7-12) 8-3

5 x 10,700 x 240 2 48 x 5 x 10 z166.38 6

+

5 (11,000 - 10,700) 240 2 48 x 5 x 'l0 x 4.5047 6

0.0772

+ 0.0799

= 0.1571 in.

3 2

+ 1120 x 0

~ 1571

+ 32p x p

M

=

M 2

M3 11,138 lb. in.

By interpolation p p772

+

0 ~ 0799 x (1 1, 138 10, 700)

(11, 000 10, 700)

= 0.1939 in.

3

+ 1120 x 0.1939

+ 320 x 0 1939 11,166 lb. in.

4 p 0772

~

0 ~ 0799

( 1 1, 1 66 1 0, 700)

(11,000 10,700) 0.2013 in.

4 f.

Convergence (Eq. 7-13)

M 11 166 11 138 p pp25 4

3 M3 ll,138 Close enough no need for check of deflection convergence.

g.

Check h/5 (Eq.

7-8) h/6

= 240/0.1963

= 1233 >>

100 Deflection requirement is satisfied 5.

Strength Calculation a.

Calculate Mid-Height Moment Under factored Load w

= 1.4. x 0.3 x 56 = 23.3'2 psf P

= 0.75 x 1.4 x P

= 1176 lbs.

pu P

P

= '0.75 x 1.4 x P

=

336 lbs.

0 0

8-4

2 "3.52 x.20 x 12

+ 1176 x 0 + 336 x p + 336 x 5

75 8

15,078 lb. in.

Since M

)

M 2

cr 2

0 0772

+ 0'0799 (15,078 10,700)

(1 1i 000 10i 700)

1. 243 in.

2

=

M3 M2 + 1176 x 1.243

+ 336 x 1.243 16,227 lb. in.

g3 p p772

+

0

~ 0799

( 1 6, 227 1 0, 700)

(1 1 i 000 lpga 700) 1.549 in.

M

= 15,078

+1176 x

336 x 1.549 2

M

= 16,509 lb. in.

4 b.

Convergence M

M 16 509 16 227 p p17 4

3 M

16>509 Close enough no need for check of deflection convergence.

c

~

Find Nominal Strenath, Mn 1) c

=

(P

+ 0.5 P

+

p bt f )/0.85/ f' o

p a

y m

(336

+ 0.5 x 1176

+ 0.002 x 12 x 5.5 x 60,000) 0.85 x 0.80 x 5000 x 12 c

= 0.2168 in.

2,)

M

= 0.858 f'c (d/2 Hc/2)

+

0 bt f d/2 n

a y

0. 85 x 0. 80 x 5000 x 12 x 0. 2168 (0. 5 x 275 0.80 x 0.5 x 0.2168)

+ 0.002 x 12 x 5.5

,, x 60,000 x 0.5 x 2.75 M

= 22,285 lb. in.

n 8-5

d..

P N

= 0.85 x 22,285

= 18,942 lb. in.

e.

Since N

"- M

= 16,509 N

= 18,942 lb. in.

4 u

n Strength requirement is satisfied EMQ4PLE 2:

The example is repeated with different properties to illustrate a design which is controlled by deflection.

Given:

A 23.8'-tall hollow brick masonry wall constructed with 5.50" units.

The fully grouted wall is simply supported at the top and bottom.

The unit weight w = 56 psf and f'

2500 psi.

The f

= 60 ksi.

The wall is reinforced m

with two 14 bundled bars spaced at 18 inches.

The roof load is 320 lb/ft applied through the ledger with a 3" eccentricity.

Required:

Determine if the wall is adequate.

Solution:

l.

Naterial Quantities a.

Nodulus of Elasticity E

= 1,000 f' 2.5 x 10 psi 6

m m

b.

Nodular Ratio n = E /E

= 29 x 10 /2.5 x 10

= 23.

6 6

6 s

m 2.

Geometric Quantities a.

Steel Ratio Based on Gross Section p

= A /st

= 0.4/18 x 5.5

= 0.004 g

S b.

Distance to Steel d = t/2 = 5.5/2

= 2'.75 in.

3.

Weights Base on b

= 12 in.

a.

Superimposed Vertical Dead Load P

= 320 lbs.

0 c

Weight of Wall w = 56 psf; lateral load

= 0.3 x 56 = 16.8 psf Total Weight of Wall P

= 56 x 1 x 23.8

= 1333 lbs/ft p

8-6

4:

Deflection Calculation a'.

Modulus of Rupture f

= 2.5 v'f' 125 psi r

m Section Modulus and Moment of Inertia Based on Gross Section b.

S

= bt /6 = 60.5 in.

I 2

3.

= bt /12 = 166.38 in.

3 4

gross c.

Moment at Cracking M

= Sf

= 7563 lb. in.

cz r

d.

Cracked Moment of Inertia 2 np d g

2 g =wnp d g

0. 2532 0.7018

'4 kd = 0.5 a +

a

+

4g

= 0.7198 in.

e.

I

=

+ np bt (d - kd)

= 12.62 in.

bkd 2

4 cr' g

Calculate Mid-Height Moment Under Service Load by Iteration Set

~

= 0.

1 2

1 P

e wh Po

~

0 N

=

+

+

P 6 +

8 2

0 2

(EQ. 7-11)

(EQ. 7-12) 2 0.3 x 56 x 23.8 x 12

+ 1333 x 0 + 320 0 + 320 x 5.75 8

M

= 15, 194 lb. in.

2=

2 Since M

)

Mcr 5M h

5 (M

M

)

}1 gross cracked h = 23.8 x 12

= 285.6 in.

~2 5 x 7563 x 285.6

~

5 x (15,194 7563) x 285.6 1

2 2

2.5 x 10 x 166.38 6

6 2.5 x 10 x 12.6223 48 0.1545

+ 2.0547

= 2.2092 in.

8-7

3 N

+ 1333 x 2.2092

+ 320 x 2.2092 2

N

= 17,373 lb.-in.

3=

By interpolation

<3 0 1545

+ 2.0547 x (17,373 7,563)

(15,194 7,563) 2.7959 in.

3 =

M4 X2 +

1 333 x 2.7959

+ 2.7959 x 320 17,952 lb.-in.

<4 0 1545

+ 2.0547 x (17,952 7,563)

(15

~ 194 7/ 563) 2.9518 in.

4 f.

Convergence (Eq.

7-13)

N M

17 952 17 373 0 0323 4

3 M

17, 952 Close enough

~ ~ed to Meek ZeXlection cone~pence g.

Check h/6 (Eq.

7-8) h/ 6 = 23.8 x 12/2.95

= 96.8 5.

Strength Calculation a.

Calculate Nid-Height Moment Under Factored Load w

= 1.4 x 0.3 x 56

= 23.52 psf u

P

= 0.75 x 1.4 x P

= 1,400 lbs.

pu P

P

= 0.75 x 1.4 x P

= 336 lbs.

ou 0

M2 23.52 x 23.8 x

12 + 1400 x 0 + 336 x 0 + 336 x 5.75 8

= 20,950 lb.-in.

8-8

Since M

> M 2

cr

~2 0.1545

+ 2.0547 (20,950 7,573)

(15i194 7,563)

= 3.759 in.

2 =

+ 1400 x 3.759

+ 336 x 3 '59

='4,844 lb.-in.

~3 0 1545

~

2 0547 (24 844 7 563)

(15,194 7,563) 4.8075 in.

>> + 1400 x 4.8075

+ 336 x 4.8Q75

= 25,931 lb.-in.

M

= 25,931 lb.-in.

4 b.

Convergence (Eq.

7-13)

M M

25 931 24 844 p p419 4

3 M

25,931 Close enough no need to check deflection convergence.

co Final Nominal Strength, Mn 1.

c =

(P

+ 0.5 P

+ pbt f )/.85< f' 0

p y

1 m

(336

+ 0.5 x 1400

+.004 x 12 x 5.5 x 60,000)

.85 x.85 x 2500 x 12 c = 0.7786 in.

2.

M

=.85/1 f'c (d/2 9 lc/2)

+

p bt f d/2 g

Y

.85 x.85 x 25QP x 12 x.7786 2.75-0>85 x.7786 2

8-9

+0.004 x 12 x 5.5 x 60,000 x0.5 x 2.75 d.

M

= 39,400 lb.-in.

n 4

M

= 0.85 x 39,400 lb.-in.

= 33,490 lb.-in.

n e.

Since M

=

M

= 25,931 g p M

= 33,490 lb.-in.

4 u

n Strength requirement is satisfied In the first example, both strength and service require-ments were satisfied although strength is the controlling factor.

While in the second

example, deflection is the major factor.

This latter design should be accepted since the deflection ratio is within 3% of the required value.

8.3 DESIGN EXANPLES USING SEAOSC YELLOW BOOK METHOD The research project was undertaken to test the design procedures outlined in the SEAOSC Yellow Book (Ref. 30) and to develop.

new techniques.

The performances of the test specimens

,and the analysis of results verify the design procedures stated in Reference 30.

In some

cases, the examples presented here modify the Yellow Book Method so that it is adaptable for masonry design.

The modifications apply to modulus of elasticity, modulus of rupture,

) factors, etc.,

and to deflection control.

8-10

S'EAOSC YELLOW BOOK ME'7 HOD w/lfh ao'di'tl onal provlsi ons for masan'esjgn S L E NDEP NESS Ah/ALYSlS P,

When Pens/on controls She ei"feet of'axi'al loaa'can be accounteo'or by adding Hht agi'a/ load fo the force I'n the reinforcing sfeel.

For the panel sho~n, the max/imurn deflection to determine the Pd effect evil!occur when the nominal moment strength M~ aP the rnidhe/ ghf of the avail r's reached.

M=Az (eif)f>> (d S/2)=-Aominelhfom Str.

Where: Aa (e ff)= Pu fAa f>> Ae for smell P~

fy hc Def /ected Panel Shape 8 = Pu +Ashy = O.BSc o.85'; s

= 0.90-2.OP /j~ Ae; for small Pneglecf second fer m:

"For v'allies of 4 For concrete and br/ ck masonry see Table 7-4.

Mu = wu hc Y8 + Pule/Z +(Pul fP~e)4n

> where 4n= +Mn hc 4B E~Z~

F~ =57 OOOO~'or normal weight con crefe.'~

= /000 f~

For concre,Pe end br/ ck /masonry l=nAa(elf)(d-c) + bc j8, and I+ =btPIZ L4'hen

/V/> 4 4M~ e'all seed/ on I's adeq uaPe For st'r engHh.

Sere/'ce Oeflecfion LI'mif=4s= h~)IOO M,

= fr Iz/y; where gt = l'/Z; For values ol fr see Table 7-4.

cr r

Af service loads: lvls =wh~i8+ Pe>>2+(PI fPe)4s 4s = 4~r + Ma M~r (4n-4e-r) m -kf, When 4s b,/too wallsecfi on safisfj'es a'eflectl'on limit 8-11

DESIGN EXAMPLE NO.3 rlz.r-u/ coecaz7Z PAezz W'ork ahecH

/ of'2 Pui Hfai'/on c'onfI'nuous t"oozing g~ = 3000 psI +28days, f> = 60,000gsI Panel Height= he = 24.0 &.,e = f/Zia.5= G.25in.

7rihutary Poof Dead Load= P, = 3ZOplF.

7rla/ seed/ on and refnforcjng:

S'e/egj P= 5+iin., Pelnf.4~9

o. e s= 020~/2/9 = 0 26 7in/)9; 0.5QpS=I 067!7 hc

" A>=b.8 =lZ'55= <6 in'; ts= Asbd= OZC 7//2*2.75=0.008p

Panel kVh=l50~55jl2=588psfj Hall Panel kVL=P~ =088"IZ=825 Se)'srni'c fOrce = w ~ 0-3" G8 8 = ZO.'GPSS

'LLTilylA7E LOAOS: (Ref LLB CSec20.09(d)),U=.75(I4Jll 7LHI87E) o, = ~.75~/.4 "320 = 93Cc PQ P= 0.75 /.4 825 = 8cc p/F; P,+P~

=IZOZpl)".=P w~ = 0.75>I.S7>ZO.G = 2S.9@sf.

NIOMINAI MObfFNT STRE'NG7H As(e/leekivs)=tv +Assay

= 1202 +.267*6!OOOO =OZ9in =Ass fp SO 0OO 8

= P +A !'

IZO!.'+I!'!!!'0 !!968

!.85F'!

.85"3

'/!'.

c = a/O.85 = 0.503/0.85=0.&OZin.

4> = 0.90 (See Table 7-'4) iyl = Ass f~ (d a/2) =029~6'!0,000(Z 7> 5a3/.s)-=.42,980 in-lb..

Pbf~ = 0.90 >4Z,980 = 38, C80in-/bs. = 38. 7 jn-Avgas 8-12

FAC7OREO UL7/MATE btOMEAIT Exam@/c. 3 York shee f 2 of'2 E,'=57000yf'7000'jl3OOO

=3,/ZOOOopsi n = Eg/IE~ = 29,000,000<<I3, /Z0,000 = S. 3 I~

= n Age (d-c) + bc <</3 Z

8

= 9. 3 ".28 7(2. 75.-662) + /Z<<. 662 I3 = /Z. 80 in.

= SM< h<

5 43.O ~24 IZ = 9.3 in.

48E I48 3]IZ>IZ80

/r/ =~

h +P,.e/2

+ (P,+P )~

8

= Z8.9 <<24

/2< Z>O i'n-lb. = 3 7. 2 /n -A ips The capacity of 38. 7 ex@'eeds /be epphecf mon+en] of 37 2, Sec'bOn QA.

CHECK OAI OEF LEC 7 /ON LIMI7A7IOhl Mfa'. 8s =h,i//00 a/ univac/ored service.loads

= 5 ~P

= 5 ~30 0 0 =2 7'/ps i; Ie = 0 t//2 = /6 0<< I'n.

A Mcr = f 'le/y<

=,.27/ /66/2.75 =/< Sin.-ki'ps

= S Mcr Ae 8" I3.2 ~ 24 "l2

. = O.975 iig.

4B Eg Ip 48'3/20

~ I6&

AP unfacHored serv/'ce loads assunve 8 =h~/]00 =Z.88 i'.

W h~i/8 W P, er/2 + (P, + P,) 8

= 20.6 <<24 '/2<</8 +320 G.ZSi/2 <<'(320+825)Z.88 I7,800 8 I OOO + 3, 300 Z2, IOO]n-lb.= ZZ./ i'r/-k]ps Ms Mcr

(<<Bn - Llcr)

Mg M(r

= 0.27s + 22. I-I<s'9. 3 -e278) = 2 /8 in

43. 0 - ld. 5 7he serw'ce deffech'on i's wi'(hi'n lt'mt'Hs, sect/on is adequaf/

8-13

I l

)

1 0

FACTOREO ULT)MATE +SORBENT E =57000~/'/000 t//3000 =3,IZO,Ooopsi n= Es/IE

=29,OOO,OOOi3,/ZO,OOO= 9.3 Z.=n A(d c)*-~ bc'l3 3

= 9.3".28>'(2 rB-.OSZ) ~/Z>>.rereZ/I3 = /2.80i R

2

= SMn Ae 5 "49.0 > Z4>/2

= 9.3 Jn.

48E I 4e 3,IZO IZeO Af =~

h, +P, Biz+(P,+P)8 8

= 28.9 '24 "/2/8 + 336 5.25IZ + /ZOZ"9.3 Exam@/e 3 W'ork sheep 2 of'2

= 24,970 9 I, OSO+ I/) I80 =37,ZOOin-lb. = 37.2 in-A.]ps 7he capac1 fy oP 38. 7 en'eeds Phc appheu'orgen] of 37.2, secban O.A.

CHECK Owl OEFLEC T]On/ Ll+I7A7!On)

/v/ax 8s = h.~iI/Oo at'nfactored service loads f=5~1'

$ ~~>OO=Z I'/ps/', I> =Ziti//2= /55 i'n.

Mcr = t'I+/y< =. 2 //<</66IZ. /5 = I6.5'n.-kiPs

= 5 Mc'r hc = 5" Ia.z ~ 24~)2

. = 0. 27Ein.

4B E< 1g

<8 '3/20 lb&

AP unfacHored servi'c'e /ops assun7e 8 =h~/]00 =Z.BB i'.

m, - w h./IB W p, BIZ ~ (p ~ p )8

= ZON "Z4 /2/8+320 6.25/Z +PZO +825)Z.BB

= I7,M7 + I OOO + 3,300 2Z,IOOin-lb.= ZZ.I in-kips t Ms-Mcr Mn Mcr

= e.?7s'+ 22./-/6 s'9.3 -0.275 ) = Z./8 in 49.0- /6'.5 7he service deflection is a&hi'n /i'rrii'f>,see/fan 7s adeqvafe.

8-13

OES/Gh/ EXAMPLE NO. 4 CpecPE7-E

~ASONRY PAiVEL I

&oik shee 6 lof'2 Des/gn based on modifi'ed 5EAOSC Ye//ow Book mt shod.

P'

/5OOpsI';

P~ = 60 OOOpsi'. S'ee sketch for EXarpple /

'Panel H~ =h< = ZO.Oft'.; e =6.3'.

Tr/buPary ]POof Oead Loao' t, =3ZOP/F Trial selecti on: 6"CALI(/= 563 ); Reinf <5g I0i"o.c.

As = 0. 3 I"l2/16 =0 233 in/fr!; Ae = b 2 = IZ"5. 63 = 6 76 i'rl.

d= BIZ=Z.8/i'n,

~

to = +~)bd=0.233/l2 2.8I=0.0069( pb

'Pane( t/Yf = G.IO =gOpsf,'f elf Panel le. = 60~ 2O/2 = GOO pl/= 9 Se/sm(c force = m = 0.3 80 = iggsF

iLILTllvlATE L0AOS: (Ref, U. 8. C Sec 260.9d); LI=.75(I40tl4L9/Q P,= 0.75-].4 aZo = sar pie P, =O.75./.4..t 00 = gSOglf P,pP,=9@@p/p= g

= 0.75"/87 /8 =z5.z ps'Omjnr<L, up~zmr S7-PENG7-H

,.j A,(effective) = i'u+Ael~ = 9cro +.233'00000 =0249in Ase t SO,OOO P &Ai = 9

%.238 0 =0&77

'85'"

b t

c = aV.85'

0. 977'. 83 = I.I49 in.

('

= 0.80 (See Table 7 4, CMUSpecial Inspection)

M=A,f (o'-a72)

= o 249 rooo.o(~ ei 9772).=3-.4,09oin Ibs =34.7in hip-s.

O'M~ =0.80 34.'7= 27.8/in-A/ ps 8-14

8 DESIGN EXAMPLE NO. Z PYork Shack l of'Z

'RICK MASONR Y PANEL Oh/ COh'7lA!L/OUS F'OOThyg presign based on moCk'fi'ed SEA OSC Yel/a+ Book medhod l800 ps/> fy GO> 000psi. See sketch for Example /.

Penel HP. = h< = Z 7.'Ofi,; 8'

8. o in.

7ri'bu]ary /Poof Dead I Oaa'= 3ZO p/P=P 7rl al a ech'on: 9 "/3ri'ck kVa/I(8=9. 0')> Rejnf ¹G ~ Ir'o. c.

Aa= 044 /2/Ia = 0.33in//7. - Bee =b/=IZ"9 =/08in d= t./2 =9/2=4.Sin.; p= A /bd =0.33/Iz 4.5 = o.oog+ pa Panel w/. = 9 " Io = 9 0pe f; Ha/f Panel &/.=9 0 ez 7/2 =/z15plf= Pz

,'. Seisrn/Ic force = W=O.3.90 = Z7psF ULTIMATE LOAOS:(Ref LI/3.L.Sac.Zro9d); L/=.75(I4JIIVLWI87E)

+ui 0.75 "//4"320 = 33K Plf P, = o.v5-I.4 (2l5=lzmplf; p, +P,= Kt2p/E=P w~ = O.7$ "/87~Z7 =37.9psF A'OMIT'AlMoMEAITST)LENGTH 3 (eeoc Be) ~p+x 2 =IBIzee.Boooo=oooo'2 CciO) OOO 8 =P 33 8 = Ie 238.33 "Bo

=I.IBB BBI II

.88'IB.O "I2 c = a/88

= I. Iae/F89 = /. 372 in 4 = 0. 70(see Table 7 4, /3rfck, Special /nspec tI'on).

AP~ = Aaa >~ (d-8/Z)

=.337 f0000(45-/ICf/2) =//3900in./b.= 83.9in-kipS O'M~= 0.70 >83.9 =58. 7]n-Alps.

~ 8-16

FACV OREO uLT]uArE MOMEAI7.

I Scampi'e 5 8/ork Shee) 8 of'8 E

= /OOC f = /OOO "/800 = I,BOO, OOO ps i n = E /E =23 00o oooo/,800,000

= /r./

I<< = n Ase (cl-c) t bc //9

= /a/.857 (~.5-/.372)'+ /2 /3 72 /3,= 5/.Blain.

8n = </V/n he

= 5 83.

27 /2

7. bat'r/.

<8E 2c..

55./9 so sect)'on is Q.K:

CRECe oN OEF LECT/ON L/M/rAT/ON

/v/ax.ds= h~/loo =8.24 "at unfactored service loads f'=2.0~P'2.0~(800

= B5Psi; IS= bi.//2 = 728 /n4 M<< = tr Ie/y~ =. 085 " 72 9/< 5 = l3. 7 7in ki ps'-

r 1cr = 5 Mcr hc: = 5~/3 77~.27*/2

= 0.//5 in.

48 E I~

W8 /8OO-72m At uncolored service loads, assume 8=bc////0=8.2yin, M~ = wh~/8+P,e/2 t(P,tP~)g

=27~27 <</2/S+320 9.0/tZ + /535a3.24

= 29,5'2O + I28O+4970 =85 770in-g. =35.Bin.-//(/ps

>s = >cr + <s-Art<<(in der))

M'n ~cr

~ //5 f 35.8 /3. 77 (7.@g-'. //5)

B3.9 /3. 7 7

=.//5 + 2.48

= 2.50 in.

The service deflection /s mi'Phin /IrniPs, section is O.A.

8-17 P

DESEGVi EZAiMLE NO.

6 Work Sheet 1 of 2 Material f'c fy P1 e

Trial t

As Panel wt.

P2 Seis.

Ultimate loads Pu1 t

Pu2 Pu "u

b8.8

&8.8 0.3 psf x

> I </2 x

68.5 Qz,o 7Z'Z x 1.4<oi74 x

1.I, X o. 7$

PU1

+

PU2 Z o. &

x 1 - 8 7 x o. 7e Coney ojg Wall on 2 aoO psi

&oooo psi 8zo plf g.'zS in.

I.o f't.

g P'all S'S in.

g xg7 sg. in./ft.

Rebar d

h S

Pp 7 ZZ plf go. & psf 9"ac t/2

=

Z 7~

b x t

y. QO&%

in.

in.

Wall wt. I mid ht..

b3 Cu 7S" Q

/ o'g4 plf psf continuous footing Nominal Moment Strength i

As Eff =

(

Pu

+

As fy

) / fy=

Pu

+

As fy

) / 85f cb a

/

.85 0.90 x', $

/o'94

+ o,a@7 x Coooc) 6 o e o oi

/ 7/oO o,gS x 2oao x /2 o.Sy /

>. <8 zuD x /4.+

wh.

x1.5

+ P1e/2

+ (P

+P2 2

u c

u1 u1 U2 2+)xZID x

1 5 +83+x

+

Io'pQ x

2

/9'. /g

+

/. oS' 9, o7

=

2,8.Q nk (

7 38 in.

7. 3$

iIK 5

M =iS7

.n Wall section is

( ~mxW ) adequate for strength requirement.

Check Deflection Limitation f

Ig Mcr

~cr 5 x

( f'~

c x12xt 1

3 f xI /y g

5Mh2-:(48E x

( 2oco

)

-" g20 psi t

=

/4o +

in.

= o.zZ4 x // & /2.7S

=

/S.S "k

5 x /3.~ x ~~ x144 g

48x 2~~D x // ~

At service load:

Assume M

=wh2x1.5 s

c Zo, gx (2I.D) x 2

h

/ 100

gS 2 / 100

2.Z 2. in.

+P1e/2+(P

+P

)D 1

2 1.5

+ 32a x

2

+ /o74 x Z.S'2 C.2s-

/d.93 +

+

0.2. I

+

o.z I

+

/. oo

+

Z. 7' M

M s

cr M

M n

cr n

cr x

( 7.08 o.2I

)

/.z7 in.

h

/

100 c

~al1 section is

( ~axe=

) adequate for slenderness requirements.

8-19

Example No.

7 Work Sheet 2 of 2

Factored Moment Icr

/ ~

z 10 psi 6

1000 f'

/

E s

m 1000 x

/go o 29000 c

)

+

b 2

/.Z X zo 3

c 3

+

x

( D,$O

)

12 3

3 4

in.

n A

ff (

d

o. 8o) 2

/'P. 3 x ~, / pg ( 0, b /

/8'. o 2

x 144 - >. 6/ in.

5x36ox 48z g~o x

3>6

+ 2o

~

32. 3 5M h>>;

(

48 E

I

)

Mu v

h x 1.5

+

P 1

e /

2 2

u c

ul a 3y,(

x

( /J.o) x 1.5, + 33&

2

+

(

P 1

+

P 2

)

7. 3 x

2

+

(

/o g Z' x~.g/

+ /.2~+

y py

~/ Z k

~

QM =z5,o Mall section is

( ~~) adequate for strength requirement.

Deflection Limitation I

g Mcr At service M

h /100 c

2.<

( f

)

2 < x

( rZoo) t5.g psi

.b t

/

12

~

x 12 x (7.ga)

~

y4 <

'3 1

4 12

'f x I

/

y

~P6P x

44%

//. 2 "k

r g

t 3.Q /

5Mh2

~ (48E I )5x //-'2x( IB.O)2x1 44 cr c

m g

48x t~o O x

44%

load:

Assume 6 i h

/

100

~

12 x

/g /

100 C

2 h

x1.5

+ Ple/2

+

(

P1

+

P

)~

c 24ox

( go) x1.5

+

32O x

2

+ (32o~ 7'2O) x v /4 2

7 3

//, b4

+ /./P

+

2.2Z

/W, /

"k M

M n

cr a>oQ

+

x

( 9Q/ - ~,aQ

)

y/o,o - I/i' y,o$

+

~ gQ a

o Qcf in ~

Mall section is

( ~~

) adequate for slenderness requir'ement.

8-20

DESIGN EXAMPLE N0.7 Work Sheet 1 of 2 Material f

~

fy Pl

/ao u psi (Called Inspection) 6o, ooo psi gzo plf in.

W U P

h C

2 Trial h

C

/g.o ft.

g C'Mc/

Rebar:

S 24 A s Panel wt.

7. 6Z in.

o, 16'q. in./ft.

g psf a t/2a g $ /, in.

2 b

x t

7. 6 +~/2, 9'/.Z in ~

o,/69' W o.gQ P2 Seis.

v Ultimate loads P

P 8o x /g o ao x

03 1.4 x 92OX'ops 9b ~

1.4 x garo,7g 7S 5 7Zo pl f z4. o psf Wall vt.

0 mid-height P

U Se is.

w U

P

+

P 2

~

/o9Z U1 U2 1 4 x 24.D

~

09.4o pl f

.psf Nominal Moment Strength A

E f

~

(

P

+

h f )/f

/o 9Z s Eff u

s y

y a

~

(

P

+

A f )/(.85f')

u s

y m

a a

85 0.80 X o,b

+o /$ $

Coo 4 oooo

/og9o

.85 x

rZoo x

12 0.85 m

o /73 in. 2

o. 8o in.

o, 6,C/.

o. 65 in.

Mn e

h f

(

d -

a /

o, /7 ~ x 4'

( >. 8 /

2

)

~o. 6 2

Z3.o 8-21

DESXGN E~iPLE NO.

8 Work Sheet 1 of 2

Materialft c fy P1 e

h c Trialt As Panel wt.

P2 Seis.

w Ultimate loads Pul Pu2 Pu wu Cc/nc/-e Ze Wall 9ooo psi 4 a.aoo psi 3zo plf 7o in.

z8.o ft.

U 7

wall

/.a in.

o. age sq. in./ft.

97. S's 87+ x 0.3 x

f

/2

87. S 32o x 1-4 x'o,r<

/Q'7Q x 1+4 g o,7~

u1

+

Pu2 a&.5 x

1

~ 4 on continuous footing Rebar:

< Z W //

d

=

t/2

= 5.S'n.

A

~

b i t

~

gg g in ~ 2 8

Pp o.4og Ya

/ giz plf Wall wt.

O mid ht ZC.3 33 Car

= /2+&

/Ccr2Z plf 3& p psf Nominal Moment Strength Mn 0.90 2.0Pu/f cAg=

"s Eff fy

~

d a/2)=

y Mn

~

o8&7x As Fff =

u

+

As fy

) /

u As fy

) /'f'cb a

/

.85

//o2g

+ 0,$ 3/

z &ooaO OOOO Yr 9oO a.pg x 3ooa x /z a,pZ /

.85 0

2 0 x /6Zi 3opo x J4

= o 96ssq. in.

o, 7Z in.

o,8) in.

o.88 7 o MS x C o (9~o-

'~ )= / 8.g "}r.

2

&/. O 8-22

Example No.

8 Work Sheet 2 of 2 Factored Moment E.

l'r 57000

( f'~

E, /

E, n

A Eff (

d c

) 2 s

2

t. > x o.~~a (S.s-oat) z4.o

+

z.4 57000 x

( 3ooo) 29000 / g/2 o

+ bc3/3

+ /z x(oap) 3 ado.4 in.4

= &,/Zx/o psi M

48x y/zo x zb,4

+

2 u

c u1 u1 u2 0&,g x zZZ' 1.5

+ 93cox

+

/ b zz.

x 2

43.O

+

y.g

+

/~.y

=

/oO.+

"k 5'Z in.

g M

Wall section is

( ~~

) adequate for strength requirement.

Check Deflection Limitation f

Ig Mcr s x

( f~

)~

c x12x t 1

3 f

x I /

r g

5M h2-:

(

x

( SooO

)

=

Z7+

psi 843 in 2 74 x 3a3

/3.Z

=

z.Q.5 "k 48 E

y

)

5 x 2&.SX 2 x144 g

48x g/zo x 34$

At service load:

Assume M

h 2x1.5

+

P c

2&3x

( Z+ )

x 1.5 2

e/2+

+ Qzox

/ 100

= 99k/

100=

3. 3 & in.

(

P1

+ P2

)~

+

/Z'<W x 9.3&

7 0 2

9o,'I

+

L +

o ~ 8o

+

Os3O

+

/./

+

M M

s cr M

M n

cr 87 '2 - 26.5 6$,$ - z.6,5 3 7 x (f.gZ.

o 3O )

g.C& in.

~lk h

/

100 c

Mall section is

( ~aszex

) adequate for slenderness requiremen<s.

8-2 3

SECTION 9

CONCLUSIONS, RECOMMENDATIONS, AND OTHER CONSIDERATIONS

9. 1 CONCLUSIONS l.

~Bucklin There was no evidence of elastic and inelastic lateral instability (buckling) for the load ranges

tested, which were primarily lateral loads with axial loads less than 1/10 of the short column axial capacity.

2.

Pe Moment Effeet.

The significance of the eccentric moment from the applied simulated light framing roof load was small.

3.

Ph Moment Effect.

The significance of the P-b, moment was most pronounced in the thinner panels but did not produce lateral instability in the load ranges tested.

Panel weight was the largest component of secondary moments.

Secondary moments accounted for approximately 20/ of the total moment at yield of the reinforcement.

4.

Load Deflection.

Load deflection characteristics of the panels can be approximated by three straight lines represent-ing the uncracked

stage, the cracked

stage, and the postyielding stage.

The intersection points of these lines are a function of the moment capacity at modulus of rupture of the concrete or of the mortar joints in masonry and the moment capacity of the wall section at yielding of the reinforcement.

Excellent correl ation of panel midspan moment versus de flec-tion plots can be obtained with test resuls by drawing a straight line from the origin to the moment at first crack and the moment at initial yield of reinforcement.

The lines represent the uncracked to cracked to yield deflection stages.

1 9-1

5.

Load Moment Curves.

The interaction P-M (Load-Moment) curves for short columns provided an adequate predicted 'moment

,capacity envelope for both masonry and concrete panels when loaded with relatively low axial loads that are much smaller than balance point on the P-M curve.

6.

EI Value.

Tests showed that the product of the cracked

~transformed section moment of inertia and the code modulus of

.elasticity was useful in predicting midspan deflection of the panel at yield level of the reinforcement.

This was true for both concrete and masonry walls.

7.

Residual Deflection.

Although the panels exhibited

,adequate strength at and beyond the yield point, the rebound "study indicates that a

midpoint.permanent deflection can be

,'expected for panels loaded to the yield level of the reinforce-

~ ment.

8.

No h t Limitation.

The tests demonstrated that there was no validity for fixed height-to-thickness limits, but they did reveal the need for deflection limits to control potential residual deflection in panels after service loads experience.

9. 2 RECOMMENDATIONS 1.

Minimum Reinforcement.

Moment capacity of cracked section at yielding of reinforcement should be greater than or at

,least equal to the moment capacity of the uncracked section based on a

gross section tensile strength of S~f'or

concrete,

2. 5JY for hollow block

masonry, and

2. 0~

for solid brick masonry.

2.

Deflection Control.

The adoption of deflection control is a

new feature and is used to assure a wall of reasonable straightness after a service level loading.

It should prevent 9-2

excessive deflection service load level, and also use of a panel with excessive flexibility. It is recommended that midheight deflection be limited to height divided by 100, that is d

=

pp.

h 3.

~Factor.

The factor has been introduced to reflect effective quality control relating to material and con-struction practices.

It is suggested the

)

factor be used to

, account for the differences in construction with continuous and

noncontinuous inspection, for both concrete and masonry construc-

, tion.

It 'is recommended that a

)

factor of 80% of the factor I

for special inspected work be used for noncontinuous inspection.

4.

Maximum Amount of Steel.

The maximum flexural steel

ratio, p

based on gross area should be limited to the value

~. given in Table 7-1, Maximum Design p

for the Units and

," Material, Shown.

This limitation on the amount of steel is to assure that there will be a ductile yielding condition and never

~ a brittle failure of the concrete or masonry.

9.3 OTHER CONSIDERATIONS 1.

Desi and Construction without Continuous. Ins ection.

All the test panels were constructed under close supervision and continuous inspection.

For construction that does not have

- continuous inspection, the current code requires that the allow-able stresses in masonry design be arbitrarily reduced by one-

• half.

In essence this provides for an increased factor of safety to cover for the uncertainty of the quality of the construction

,and material.

Some of the concerns were the strength of the materials and the location and yield strength of the steel.

Computer studies were made to determine the capacity of numerous walls where 9-3

these variables were considered.

For

• all economically practical configurations, these computer studies conclusively showed that compressive stresses in the masonry and concrete were not the limiting criteria.

However, the

amount, the location, and the yield strength of the reinforcement always governed the

'ultimate capacity of the walls.

0 The consensus of the Committee was that construction without continuous inspection can be handled by an adjustment of the factor in the design.

By reducing 'the

)

factor, the adjustment is made on the resistance side of the design equ'ation.

This more properly reflects the original intent of the

)

. factor, rather than changing the loading side of the design equation.

The suggested

)

factor has been reduced to an amount that will adjust. for these variations of materials and workmanship, includ-

'ing steel location.

The resulting design penalizes uninspected walls by approximately 15% in height.

This means that for the same amount of steel, the uninspected walls would have to be 15%

'shorter-than inspected walls of the same thickness.

This suggested method of design recognizes the large amount of construction built throughout the United States where continu-ous inspection iz wot available or is not used, and provides a

guide to architects and engineers for the design of concrete and masonry walls without continuous inspection.

2.

Partiall Grouted Walls.

The masonry walls tested were all solid grouted.

In pactice, many walls are not solid grouted hut are only grouted at the steel location.

Although all walls tested were solid

grouted, the same principles of design and performance should prevail for walls that are only partially grouted.

From the analysis it was evident that the stress block usually falls within the face shells only and thus the lack of grout in some of the cells does not influence the performance of

the wall.

The cells containing steel would be grouted and thus, through the grout, the steel would be functioning.

This 'is the

.mechanism by which even solid grouted walls function.

For partially grouted walls, the actual moment of inertia should be used for uncracked

sections, while the transformed computed moment of inertia used for cracked sections can be used even for partially grouted walls.

The depth of the compression stress block should be calcu-lated to determine that it is completely within the face shell of the masonry unit.

If it isn',

computations can be 'made to evaluate the section based on T-beam configurations in which the face shell is the flange and the grouted cell is the stem.

0 3.

Moment, Determination.

The analysis of the test panels

~'i'roperly considered that the walls were pinned at the top and the 2

" bottom.

Therefore, the lateral moment on the wall was WH /8 lf and this became the basic design moment to which the Pe and

'D effect were added.

The designer may wish to modify these

,< moments and deflections to take into account any conditions of

.restraint.

4.

Precast vs. In-Place Construction.

It is important to note that this test program covered both the precast elements (concrete) and the construction in-place elements (masonry

, walls),

and they were all on continuous footing.

Therefore, the Ill

, scope of the program applies to the prefabricated and precast

.walls, and to the constructed in-place and cast-in-place walls.

. No differences were noted in the test performance characteristics between the precast concrete panels and the built in-place masonry panels.

9-5

\\

I 0

P)

the wall.

The cells containing steel would be grouted and thus, through the grout, the steel would be functioning.

This is the mechanism by which even solid grouted walls function.

For partially grouted walls, the actual moment of inertia should be used for uncracked

sections, while the transformed computed moment of inertia used for cracked sections can be used even for partially grouted walls.

The depth of the compression stress block should be calcu-lated to determine that it is completely within the face shell of the masonry unit.

If it isn',

computations can be made to evaluate the section based on T-beam configurations in which the face shell is the flange and the grouted cell is the stem.

3.

Moment Determination.

The analysis of the test panels properly considered that the walls were pinned at the top and the bottom.

Therefore, the lateral moment on the wall was WH /8 and this became the basic design moment to which the Pe and Pb, effect were added.

The designer may wish to modify these moments and deflections to take into account any conditions of restraint.

4.

Precast vs. In-Place Construction.

It is important to note that this test program covered both the precast elements (concrete) and the construction in-place elements (masonry walls),

and they were all on continuous footing.

Therefore, the scope of the program applies to the prefabricated and precast

walls, and to the constructed in-place and cast-in-place walls.

No differences were noted in the test performance characteristics between the precast concrete panels and the built in-place masonry panels.

9-5

5.

0 enin s in Halls.

The walls tested were solid walls, and it is recognized that walls with openings and other configu-

~

rations may introduce special problems.

This publication and the research program did not cover these considerations, but it is suggested that the engineer and designer use basic principles for the analysis of walls with openings.

It should be recognized that walls with openings will have a change of stiffness caused by the openings in the walls.

The design of opening jambs deserves special consideration.

6.

Isolated Footin s.

The test program was conducted so that all walls had continuous support.

A technique of designing walls on isolated footings is given in Reference 30.

Until further testing is

done, this appears to be an acceptable approach for evaluating slenderness effects in the design of

tall, slender walls on isolated footings.

Special considera-tions should be given to the increased loading on the wall elements over the isolated pads.

10.3 CONTRIBUTORS Numerous organizations and individuals provided materials, technical

services, and money that made this project possible.

Listed below are the organizations and individuals who provided

'his support,.

" Associated Concrete Products t

Baldi Brothers Construction Co.

" Bethlehem Steel Corporation Wallace Bonsall C.E.

Buggy, Inc.

~ Cabot, Cabot

& Forbes California Field Iron Workers Trust Fund

,.'alifornia Gunite Co.

, California Portland Cement Co.

Ted Christensen, S.E.

~

, Concrete Coring Company Concrete Masonry Association of California & Nevada

Conrock Company Correia

& Christian Dominion Construction O.K. Earl Corporation Eide Industries Emkay Development Foster Sand

& Gravel.

Hillman, Biddison & Loevenguth, S.E.

Higgins Brick Co.

Incentive Builders Investment Building Group Tom Kamei

& Associates, S.E.

Kariotis & Associates, S.E.

Keller Construction Co.

Masonry Institute of America McLean & Schultz, S.E.

Millie and Severson Mr. Crane, Inc.

Mutual Building Materials Osborne Laboratories Charles Pankow Co.

Portland Cement Association Ramtech Laboratories Rockwin Corporation Sanchez and Hernandez S

& H Steel Smith-Emery Co.

Spancrete of California

Stolte, Inc.

Donald Strand, S.Z.

Superior Concrete Accessories, Inc.

'Syart Construction Co.

Synetic Designs Company Thompson and LaBrie, S.E.

Transit Mix Concrete Triangle Steel Trus Joist Corporation Twining Testing Laboratory Davis Walker Corporation Warner Company Watson Land Development Co.

Paul Winter, S.E.

Wray Construction Co.

Wheeler

& Gray, S.E.

10-2

10.4 DOCUMENTARY FILM The Masonry Institute of America made a special contribution by producing a documentary film on the test project.

MIA engaged White Productions to make a cinematic record of all phases of the project:

committee

meetings, laboratory testing, instrumenta-tion, testing of panels, and descriptions of uses for masonry and concrete walls.

The films have been reproduced

'so that many organizations throughout the United States can show this research program to thousands of architects, engineers, building officials and constructors across the country.

10.5 STAFF SUPPORT The Task Committee is pleased to recognize the special dedi-cation and support given the project by the staff members of the Masonry Institute of America, namely Juan Giron, staff engineer, for computer

studies, drafting, designing, and other technical

.assistance, and Bella Sokoloff, for secretarial and editing support."

They worked unstintingly for the project from its beginning to the final report production.

Our success shows up in their work.

10.6 VOLUNTEERS There was much discussion in the committee as to whether to engage a testing laboratory to conduct the total test under the supervision of the committee or to have the committee do the testing itself.

Under the guidance of project director Ralph S.

McLean, structural

engineer, of the firm McLean S

Schultz, the program was set up and the members of the committee volunteered to serve as his assistants to conduct the program.

Jim Amrhein, member of the committee, was present at the testing of almost every wall.

Robert G.

Thomas of the Masonry Institute of America and Robert Tobin of Portland Cement Assoc.

(and member of the committee) were at the test site as often as possible.

10-3

y 4 ~

In addition to the basic cadre of committee

members, volunteers from numerous offices assisted in the program.

The

. volunteers were members of the Structural Engineers Assoc.

of Southern California or the Southern California Chapter of-American Concrete Institute or interested engineers and building officials who wished to participate in the program.

The Masonry

~ Institute of America scheduled these volunteers so that there would be approximately three at the test site for each test.

,~ Without Mesc volunteers this program could not have come Co fruition.

They helped set up the test panels and equipment, conduct the tests, and read the many gages,

dials, and controls.

Listed below

'pologize to those names that we have

'costa, Julio

~

~

'leem,

-Syed

,, Allen, Jr.,

C.K.

Amanullah, S aced

-,.Austin, Mary

Halwani, Sammy

Harder, Ben Hart, Stanley

Hatalsky, Pete

Hobbs, Leonard

Meeker, Edward Meier, Mike Milczewski, Juergen Mills, Gary

Muneno, Don is a partial list of the volunteers.

We whom we missed, but we have included all the available.

'Baumann, Harms

Bayer, Jack

Beer, Robert Bliel, Richard Choy, Phil

Corbett, John

Crask, Lloyd Christensen, Ted

Czapski, Dan

Daniels, Robert 4w'Dickey, Walter DiMundo, George

'Eggenberger, Byrne Freyermouth, Ed Gutierrez, Sr.,

Ramon

Jasper, Richard

Jones, Mike

Juvier, Arizmendiz

Kamai, Tom Kariotis, John Kobbitz, Steve Kobzeff, John

Korman, Ben

Lam, Howard

Lambe, Michael tl

Lamont, Wayne

Leuer, John I ue, Raymond Mann, Cliff Martin, Melvin

Narver, David

Negen, Tom

Nieblas, Gerald

Ochoa, Ignacio

Osborne, Howard

Osborne, Raymond

Pach, Greg

Powers, J.C.

P fefferie, Warren

Pullman, George

Ramos, Rack Rao, J.K.

Reyes, Joel

Rez, Don Richardson, R.C.

10-4

n

'~

~

i

) ~

In addition to the basic cadre of committee

members, volunteers from numerous offices assisted in the program.

The volunteers were members of the Structural Engineers Assoc.

of Southern California or the Southern California Chapter of-American Concrete Institute or interested engineers and building officials who wished to participate in the program.

The Masonry Institute of America scheduled these volunteers so that there would be approximately three at the test site for each test.

Without these volunteers this program could not have come to

'ruition.

They helped set up the test panels and equipment, conduct the tests, and read the many gages,

dials, and controls.

Iisted below is a partial list of the volunteers.

We apologize to those whom we missed, but we have included all the names that we have available.

Acosta, Julio Aleem',

Syed Allen, Jr.,

C.K.

Amanullah, Saeed Austin, Mary

Baumann, Harms

Bayer, Jack

Beer, Robert Bliel, Richard Choy, Phil

Corbett, John Crask, Iloyd Christensen, Ted

Czapski, Dan

Daniels, Robert

Halwani, Sammy

Harder, Ben Hart, Stanley

Hatalsky, Pete

Hobbs, T.eonard

Jasper, Richard

Jones, Mike

Juvier, Arizmendiz

Kamai, Tom Kariotis, John Kobbitz, Steve Kobzeff, John

Korman, Ben

Dam, Howard

Iambe, Michael

Meeker, Edward Meier, Mike Milczewski, Juergen Mills, Gary

Muneno, Don Narver, David

Negen, Tom

Nieblas, Gerald

Ochoa, Ignacio

Osborne, Howard

Osborne, Raymond

Pach, Greg

Powers, J.C.

Pfefferle, Warren

Pullman, George Dickey, Walter DiMundo, George Eggenberger, Byrne Freyermouth, Ed Gutierrez, Sr.,

Ramon

Iamont, Wayne

Leuer, John

Iue, Raymond Mann, Cliff Martin, Melvin

Ramos, Rick

Rao, J.K.

Reyes, Joel

Rez, Don Richardson, R.C.

10-4

Sanders, Hank Schneider, Robert Scott Jock

Seltzer, Warren

Shakeri, Sirous Sinbel, Aly

Spencer, Allan Stockinger, Herb

- Stapenhill, Jim

,Tandoc, Rosalinda

Taubman, David Tawfik, Mohamed

Test, C. Taylor

Teal, Edward

Thomas, Robert G.

Thomsen, Sheen Ting, Raphael Traw, Jon Valenzuela, Louis

Warren, Jack White, Dean

Wong, Ken Woody, Hal Wu, Jackson Wyatt, Jesse

Yaguchi, John

Yee, Ben

Yeung, Herb 10. 6 REFZHG'NCES ACI 318-77, "Building Code Requirements for Reinforced Concrete,"

American Concrete Institute, Detroit, MI.

3.

ACZ Committee 531, "Building Code Requirements for Concrete Masonry Structures,"

ACI Journal, Aug 1978.

ACI Committee

533, "Design of Precast Concrete Wall Panels,"

ACI Journal, Jul 1971.

'5.

ACI Committee 533, "Fabrication, Handling and Erection of Precast Concrete Wall Panels,"

ACI Journal, Apr 1970.

ACI Committee 533, "Quality Standards and Tests for Precast Concrete Wall Panels,"

ACI Journal, Apr 1969.

ACI Committee 533, "Selection and Use of'aterials for Precast Concrete Wall Panels,"

ACI Journal, Oct 1969.

8.

9.

Allen, D. and A.I. Parme, Discussion af'aper Tiled "Buckling Design Curves for Concrete Panels with all Edges Continuously Supported,"

ACI Journal, Mar 1976.

Amrhein, J.E.,

Reinforced Masonry Engineering Handbook, Masonry Institute of America, Nov 1982.

Amrhein, J.E.,

"Slender Walls Research Program by California Structural Engineers,"

The Masonry Society Journal, 1:2, Jul-Dec 1981.

'0.

Bljuger, "Nonlinear Concrete Wall Characteristic of Signifi-cant Importance in Structural Analysis," ACI Journal, Jun 1978..

Bljuger, "Stressed State Analysis of Concrete Walls," ACI

Journal, Jul 1977.

10-5

'0 27.

28.

29.

30.

Oberlander, G.D.

and N J. Everard, "Investigation of Rein-forced Concrete Walls," ACI Journal, Jul 1977.

Popov, E., Mechanics of'aterials, 2nd Ed.,

New York, Prentice-Hall, 1967.

Portland Cement Association, "Design of Deep Girders,"

Concrete Informati on,

IS079, 01D.

SEAOSC, Recommended Tilt.-Up Wall Design, (Yellow Book),

Jun 1979.

31.

32.

'3.

34.

36.

37.

SEAOSC, Technical 'Bulletin 'No. 2, Tilt-Up Constructi on, Oct 1949.

Selna, L.G., "Slender Wall Tests Instrumentation and Results,"

-Proc.

SEAOC Convention,

Coronado, CA, Sep 1981.

Swartz, S.E.

and V.H. Rosebraugh, "Buckling Design Curves for Concrete Panels with All Edges Continuously Supported,"

ACI Journal, Sep 1975.

Swartz, S.E.,

V.H. Rosebraugh, and M.Y. Berman, "Buckling Tests on Rectangular Concrete Panels,"

ACI Journal-,

Jan 1974.

Taner, "Strength and Behavior of Beam-Panel Tests and Analysis," ACI Journal, Oct 1977.

Thompson, J.H.,

"Design of Concrete Wall Panel for Lateral Loads,"

ACI Seminar, 1968.

Timoshenko, S.

and J.

Gere, Theory of'lasti c Stabili ty, New York, McGraw-Hill, 1961.

38.

39.

Uni form Building Code,

1979, 1982 eds.,

International Conference of Building Officials, Whittier, CA.

Weiler, G.

and N. Nathan, Design of'ilt-Up Concrete Vali

Panels, University of British Columbia Report, Vancouver,

Canada, 1979.

40.

Wyatt, J.R.,

"Review of the Simplified Design Method for Tilt-Up Concrete Walls," Building Standards, ICBO, Whittier, CA, May-Jun 1980.

41.

Timoshenko, S., Advanced Strength of Hateria7s, vol. 2, Van Norstrand Co.,

1956.

10-7

~ ~