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TitleStructural Elements for Architects and Builders: Design of columns, beams, and tension elements in wood, steel, and reinforced concrete
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Table of Contents
                            Structural Elements for Architects and Builders
Copyright Page
Contents
Preface
List of examples
List of appendices
CHAPTER 1 Statics
	Tributary areas
	Equilibrium
	Reactions
	Internal forces and moments
	Indeterminate structures
	Strength of materials
CHAPTER 2 Loads
	Dead loads
	Live loads
	Environmental loads
CHAPTER 3 Material properties
	Wood
	Steel
	Reinforced concrete
CHAPTER 4 Sectional properties
	Wood
	Steel
	Reinforced concrete
CHAPTER 5 Design approaches
	Allowable stress design
	Strength design
CHAPTER 6 Tension elements
	Wood
	Steel
	Reinforced concrete
CHAPTER 7 Columns
	Wood
	Steel
	Reinforced concrete
CHAPTER 8 Beams
	Deflection
	Bending stress
	Shear stress
	Wood
	Steel
	Reinforced concrete
CHAPTER 9 Connections
	Wood
	Steel
	Reinforced concrete
Appendix 1: Tables for Chapter 1 (statics)
Appendix 2: Tables for Chapter 2 (loads)
Appendix 3: Tables for Chapter 3 (material properties)
Appendix 4: Tables for Chapter 4 (sectional properties)
Appendix 5: Tables for Chapter 5 (design approaches)
Appendix 6: Tables for Chapter 6 (tension elements)
Appendix 7: Tables for Chapter 7 (columns)
Appendix 8: Tables for Chapter 8 (beams)
Appendix 9: Tables for Chapter 9 (connections)
Appendix 10: Unit abbreviations and conversion
References
Glossary
	A
	B
	C
	D
	E
	F
	G
	I
	J
	K
	L
	M
	N
	P
	R
	S
	T
	U
	V
	W
	Y
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	K
	L
	M
	N
	O
	P
	R
	S
	T
	U
	V
	W
	Y
                        
Document Text Contents
Page 2

Structural Elements for
Architects and Builders

Page 200

185

6. From Equation 8.26, check that the stress block depth, a , falls within slab thickness:
a � ρ f y d /(0.85 fc
) � 0.00270(60)(14)/(0.85 � 5) � 0.53 in. � slab thickness � 3 in., so
T-beam assumptions are valid.

7. From Equation 8.21, compute steel area: A s � ρ bd � 0.00270(48)(14) � 1.81 in
2 .

8. From Tables A-4.10 and A-4.11, we select steel reinforcement, as shown in Figure 8.48 :
two No. 9 bars with A s � 2.0 in

2 .
9. From Table A-4.11, check whether this choice fi ts within the beam web (or stem) width of

12 in. Two No. 9 bars require 7.58 in., so the choice works in a 12-in.-wide beam.
10. The steel ratio has already been checked (step 5). The check for defl ection control is the

same as for negative moment and need not be repeated.

Shear
Wood and steel beams are generally designed for bending and checked for shear.
If a beam selected for bending cannot safely resist the shear stresses, a larger sec-
tion must be used. Reinforced concrete beams are almost never acceptable for shear
after they are designed for bending, because shear stresses, combined with bending
stresses, produce diagonal tension within the beam. Since concrete is so weak in
tension, excessive shear (really diagonal tension) would cause the beam to fail cata-
strophically. Rather than increase the size of the cross section to the point where
the concrete can safely resist all diagonal tension stresses, shear (web) reinforce-
ment is used where the shear stress exceeds the capacity of the concrete.

Web reinforcement, consisting of U- or rectangular-shaped steel stirrups, is gener-
ally made from No. 3 or No. 4 bars, bent as shown in Figure 8.49 . The force resisted
by each stirrup is based on an area twice the size of the bent bar, or 2 A s , since two
prongs of each stirrup are present at any diagonal tension crack ( Figure 8.50 ). Thus,
assuming that diagonal tension cracks form at a 45 ° angle, the number of stirrups

FIGURE 8.48
Bar selection for positive moment in T-beam for Example 8.10

Reinforced concrete

Page 201

186 CHAPTER 8 Beams

resisting tension within each crack is d/s , where d � the effective depth of the beam
and s � the stirrup spacing.

At failure, corresponding to yielding of the stirrups, the total force resisted by
the steel web reinforcement is, therefore, equal to the number of stirrups times the
force resisted by each; that is, V s � ( d / s )(2 A s f y ) or:


V A f d ss s y� 2 /

(8.36)


where

V s � the total force resisted by web reinforcement

d � the effective depth of the beam

s � the stirrup spacing

A s � the area of the reinforcing bar from which the stirrup is made

f y � the yield stress of the reinforcing bar, 60 ksi in all text examples

FIGURE 8.49
Typical web steel (stirrups) to resist diagonal tension associated with shear stress in beams

FIGURE 8.50
Assumed crack geometry for calculation of web steel capacity to resist shear forces (at diagonal
tension cracks)

Page 399

384 Index

G
Gage , 88
Girder , 2 , 3 , 4 , 5 , 157 , 162 , 193 , 242
Glued-laminated lumber , 64 , 65 , 139 , 265 , 266 , 267 ,

268 , 271 , 272 – 3 , 274 , 277 , 278 , 279
Grain , 63 , 65 , 198 , 222 , 224 , 225
Gust factor , 52

H
Hinge , 9 , 10 , 12 , 29 , 193 , 194 , 226
Hinge, internal , 13 – 14
Hollow structural section (HSS) , 69 , 75 , 163 , 302 , 304
Hook , 241 , 242 , 243 , 372

I
I-joist , 67
Importance factor , 46 , 50 , 254 , 257 , 263
Indeterminate , 7 , 29 , 31 – 3 , 171
Inelastic , 69 , 115 – 17 , 155
Infl ection, point of , 244

K
Knot , 63 , 64 , 65

L
Lag screw , 90 , 92 , 194 , 195 , 198 , 201 , 212 , 222 ,

347 , 348
Laminated veneer lumber (LVL) , 65 – 6
Lap splice , see Splice
Leeward , 48 , 52 , 54 , 255 , 256
Length, effective , 98 , 122 , 139 , 233 , 317
Length, unbraced , 108 , 110 , 117 , 122 , 153 , 154 ,

156 , 157
Lignin , 63
Line of action , 8 , 11
Linear , 1 , 57 , 61 , 62 , 132 , 133
Live load , see load, live
Live load element factor , 42
Live load reduction , 6 , 42 , 43
Load , 1 , 2 , 39 – 60 , 65 , 82 , 83
Load, concentrated , 4 , 5 , 139
Load, dead , 39 – 41
Load, distributed , 2 , 3 , 23
Load, earthquake , 46
Load, environmental , 46 – 60 , 253
Load, live , 41 – 5 , 46 , 252
Load, seismic , 54 – 60
Load, snow , 46 – 9 , 254
Load, wind , 49 – 54
Load factor , 80 – 1 , 199 , 311
Load path , 6 – 7 , 57

Load resistance factor design , 81
LRFD , see load resistance factor design
Lumber, dimension , 73 – 4 , 139 , 140 , 147 , 265

M
Main member , 90 , 196 , 213 , 217 , 360 – 4
Method of sections , see Section method
Modulus of elasticity , 61 , 62 , 68 , 132 , 279 , 280
Moisture content , 64 , 199
Moment , 17 – 31 , 107 , 108 , 134 – 5 , 140 , 142 , 161
Moment, elastic , 132 , 151 , 152 , 153 , 154
Moment, internal , 10
Moment, plastic , 133 , 135 , 151 , 152 , 153 , 154 , 156
Moment arm , 11
Moment of inertia , 34 – 5

N
Nail , 90 , 193 , 194 , 196 , 198 , 200 , 201 , 215 , 222 , 223
Neutral axis , 63 , 132 , 133 , 137 – 8
Newton, Isaac , 1 , 7
Nonlinear , 57 , 61 , 132 , 133 , 166

O
Open-web steel joist (OWSJ) , 69 – 70
Oriented strand board (OSB) , 67

P
Parallel strand lumber (PSL) , 66
Period , see Fundamental period of vibration
Plastic , 36 , 61 , 151 , 153 , 154
Plate , 194 , 195 , 209 , 237
Plate, gusset , 97 , 100
Plate, pin-connected , 99 , 103 – 4
Plywood , 66 , 67
Ponding , 129
Posts and timbers , 73 , 266 , 268 , 272 , 288
Pressure, velocity , 49 , 50 , 51 – 2

R
R-value , 47
Radius of gyration , 37 , 98 , 108 , 122
Reaction , 1 , 9 , 10 – 17
Rebar , see Reinforcing bar
Redundant , see Indeterminate
Reinforcement ratio , 121 , 126
Reinforcing bar , 70 , 75 , 164 , 165 , 175 , 176 , 177 , 193 ,

238 , 239 , 244
Response modifi cation factor , 56
Roof , 1 , 46 – 7 , 194
Rupture , 68 , 87 , 97 , 98 – 9

Page 400

385Index

S
Sag , 14 , 16
Section method , 28 – 9
Section modulus , 36 , 134 – 5 , 151 , 153
Seismic , see Earthquake
Seismic design category , 259 , 263
Seismic load , see Load earthquake
Seismic response coeffi cient , 263
Seismic weight , see Weight seismic
Shear , 18 , 19 , 22 , 23 , 91 , 145 , 157 – 9 , 185 – 91 , 196 – 221 ,

228 , 229
Shear, double , 196 , 198 , 199 , 206 , 209 , 217 , 361 , 363
Shear, single , 196 , 197 , 198 , 201 , 204 , 212 , 215 ,

360 , 365
Shear lag , 97 , 313
Shrinkage (of concrete) , 71 , 178
Side member , 196 , 198 , 199 , 365 , 366 , 367
Sign convention , 10 , 11 , 13
Slenderness ratio , 98 , 108 , 110 , 115 – 16
Space frame , 70
Spandrel , 2 , 4 , 5
Spiral , 76 , 77 , 121 , 245 , 328
Splice , 97 , 244 , 245 , 246 , 247
Stagnation pressure , see Pressure velocity
Statics , 1 – 37 , 249 – 50
Steel , 61 , 68 – 70 , 74 – 5 , 96 – 104 , 115 – 20 , 121 , 150 – 64 ,

226 – 38
Steel ratio , see Reinforcement ratio
Stiffness , 33 , 35 , 55
Stiffness, relative , 7
Stirrup , 76 , 185 , 186 , 187 , 189
Story, soft , 57
Story, weak , 57
Strain , 61 – 2 , 68 , 123 , 132 , 133 , 165 , 166
Strength , 33 – 7 , 70 , 109 , 122 , 151 , 165 , 234
Strength, cylinder , 70 , 104 , 167
Strength design , 80 – 5 , 150 , 153 , 168 , 187 , 311
Strength reduction factor , 80 – 1 , 312
Stress , 61 , 68 , 79 , 151 , 153
Stress, axial , 87 , 107
Stress, bending , 130 – 8
Stress, buckling , 108 , 109 , 115 , 116
Stress, compressive , 69 , 70 , 107 , 109 , 224
Stress, residual , 68 – 9 , 115
Stress, shear , 92 , 136 , 137 , 138 , 139 , 157 , 185
Stress, tension , 90 , 133 , 157 – 8 , 164 – 5
Stress block , 44 , 168 , 171 , 173

Stringers , see Beams and stringers
Structure, axial-force , 18 , 28 – 9 , 30
Structure, plane , 7 , 8
Structure, rigid-body , 9
Stud , 69 , 73
Symmetry , 7 , 10 , 36 , 232

T
Tear-out, group , 91 , 92 , 94 , 315
Tear-out, row , 91 , 92 , 94 , 315
Tension , 22 , 64 , 87 – 105 , 229 , 238 – 44 , 244 – 5 , 265 ,

284 , 313
Tension-controlled , 173 , 343
Ties , 121 , 328
Timbers , 73 , 141
Truss , 28 – 9 , 67 , 100

U
Under-reinforced beam , 165 , 166 , 173 , 175
Units , 1 , 375 – 6
Unserviceable , 129

V
Velocity pressure , see pressure, velocity

W
Weight, seismic , 55 , 58 – 9 , 60
Weld , 98 , 193 , 226 , 230 – 8
Weld, fi llet , 230 , 231 , 232 , 233 – 4 , 371
Weld, groove , 230
Weld, plug , 230
Weld, slot , 230
Whitmore section , 97 , 98
Whitney, C.S. , 167
Wind , 1 , 4 , 6 , 46 , 51 , 52 , 194
Wind speed , 46 , 49 , 50
Windward , 51
Wood , 61 , 62 , 63 – 7 , 73 – 4 , 89 – 96 , 109 – 15 , 139 – 50 ,

185 , 194 – 226
Workability , 71

Y
Yield limit equations , 199
Yielding , 68 , 69 , 96 , 97 , 98 , 115 , 122 , 158 , 165 , 173 ,

186 , 198

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