Answers to supplementary problems part 2: Δ Wa δ 2.16 in upward δ δ

Answers to supplementary
problems part 2
Chapter 1
The degree of indeterminacy of the frames are:
S1.1
D1
S1.2
D1
S1.3
D 12
S1.4
D 22
S1.5
(i) D 7
(ii) D 7
S1.6
(i)
(ii)
(iii)
(iv)
D3
D0
D0
D0
S1.7
(i)
(ii)
(iii)
(iv)
(v)
D5
D9
D3
D1
D1
Chapter 2
S2.1
wa4(4l/3a 1/3)/8EI
S2.2
2.16 in upward
S2.3
2 0.114 in
3 0.068 in
W 16.75 kips
S2.4
H/V 0.65
S2.5
4 0.59 in
Structural Analysis: In Theory and Practice
600
S2.6
M12 138 kip-in

M21 102 kip-in
M23 112 kip-in
M32 128 kip-in
Q12 Q21 Q23 Q32 2 kips
3 907,200/EI 480/AG
S2.7
M1 20tEI/al2
V1 20tEI/al3
M1 80tEI/a2l4
Chapter 3
S3.1
P24 32.66 kips compression
S3.2
P24 1.07 kips tension

S3.3
P13 W/(5.407 0.472a2A/I) compression
S3.4
P34 11 kips compression
S3.5
P12 132 kips tension
S3.6
H 62.5 kips
S3.7
H 8.28 kips
S3.8
H 0.166W
S3.9
T 20.5 kips
Chapter 4
S4.1
M1 Wab2/l2
S4.2
1 5Wl2/128EI
3 3Wl3/256EI
S4.3
2 wa3(l a/4)/6EI
S4.4
M12 0.345M
M21 0.147M
S4.5
M12 47.5 kip-ft

M21 31.3 kip-ft
Answers to supplementary problems part 2
S4.6
M12 25.74 kip-ft

M21 32.45 kip-ft
S4.7
M12 101 kip-ft

M21 113 kip-ft
S4.8
M12 Pab(a b)/l2

M21 Pab(a b)/l2
S4.9
M12 Pb(l2 b2)/2l2
S4.10
M12 21.45 kip-ft

M21 7.10 kip-ft
601
Chapter 5
S5.1
x/l
V2
S5.2
0.2
0.36
0.4
0.64
0.6
0.84
0.8
0.96
1.0
1.00
For member 12
x/l
M2/l
0.2
0.048
0.4
0.084
0.6
0.096
0.8
0.072
0.2
0.064
0.4
0.072
0.6
0.048
0.8
0.016
For member 23
x/l
M2/l
S5.3
x
H1
0
0.153
20
0.264
40
0.375
60
0.462
80
0.486
5
0.069
6
0.055
S5.4
Panel point
R1
1
1.000
Chapter 6
S6.1
M12 0.345M
M21 0.147M
2
0.610
3
0.264
4
0.000
7
0.000
602
S6.2
M12 47.6 kip-ft

M21 31.3 kip-ft
S6.3
M12 2.54 kip-ft
S6.4
M12 25.7 kip-ft

M21 32.5 kip-ft
S6.5
M12 101 kip-ft

M21 133 kip-ft
S6.6
M12 Pab2/l2
M21 Pba2/l2
S6.7
M12 Pb(l2 b2)/2l2
S6.8
s12 0.275EI
c12 0.444
M12 21.55 kip-ft
M21 7.05 kip-ft
S6.9
H 1.08 kips
S6.10
M 34.4 kip-in
S6.11
M12 44 lb-ft

M21 36 lb-ft
Chapter 7
S7.1
V2 7.60 kips
V3 8.32 kips
V4 2.08 kips
S7.2
M1 19 kip-in
V1 2.68 kips
H1 0.48 kips acting to the right
M4 38 kip-in
V4 3.32 kips
H4 1.9 kips acting to the left
S7.3
M2 1682 kip-in
M3 421 kip-in
S7.4
M2 3.5 kip-in
M1 10.5 kip-in
M3 0.7 kip-in
S7.5
M2 75 kip-ft
M3 50 kip-ft
S7.6
M2 9.1 kip-ft
M3 13.5 kip-ft
M4 15.1 kip-ft
S7.7
M2 197 kip-in
M3 237 kip-in
S7.8
M12 138 kip-in

M21 102 kip-in
M23 112 kip-in
M32 128 kip-in
M36 128 kip-in
M25 214 kip-in
P25 0 kips
Q12 2.00 kips
Q23 2.00 kips
Q36 2.13 kips
Q25 3.57 kips
S7.9
M12 687 kip-ft

M21 811 kip-ft
M23 347 kip-ft
M32 154 kip-ft
M34 257 kip-ft
M43 242 kip-ft
M45 239 kip-ft
M54 259 kip-ft
S7.10
M12 322 kip-ft

M21 277 kip-ft
M23 184 kip-ft
M32 415 kip-ft
M34 652 kip-ft
M43 548 kip-ft
603
604
S7.11
M21 225 kip-ft

M23 28 kip-ft
M32 80 kip-ft
M34 14 kip-ft
M43 22 kip-ft
Chapter 8
S8.1
M30 1351.7 712.8 2064.5 kip-in

V30 94.7 40.5 135.2 kips
S8.2
M1 153 kip-in
S8.3
kW 190
S8.4
P47 8.6 kips
S8.5
(i) lm lp/120 0.133(EbIb/AtEt)1/3

(ii) M6 250y12/(5) 50y34/(5) 150y5
(iii) The inuence line ordinates for M6 are:
x,ft
I L ordinates for M6
0
40.5
50
21.0
100
0
150
21.0
Chapter 9
S9.1
l/a 3.17
w 58.5Mp/l2
S9.2
S 14.8 in3
S9.3
W/H 8/3 for the beam mode

W/H
2/3 for the sway mode
2/3 W/H 8/3 for the combined mode
S9.4
Mp 9.42 kip-ft for the columns

Mp 18.84 kip-ft for the beams
S9.5
Mp 25 kip-ft for the posts

Mp 50 kip-ft for the chords
S9.6
Mp Wl
x2 5Mpl2(5)0.5/24EI
200
41.8
250
65.2
S9.7
(i) W 2.0Mp/a
(ii) W 3Mp/a
(iii) W 2.80Mp/a
S9.8
Mp Wa/2
605
Chapter 10
S10.1
The stiffness matrix is:

P 2
20
EI/l

P 3
6
28
2

3
The final moments are:

M12
M21
M34
M43
S10.2
42.75 kip-in
85.5 kip-in
236.6 kip-in
181.7 kiip-in

P 2
8
EI/l

P1
2
2 2

4 1
The final moments are:

M21 12 /7 kip-ft
M32 12 /14 kip-ft
S10.3

P 2
8
P 3
2
EI/l
P 4
0
lP
x 2
6
x2 0.136l 2 /EI
4 0.477l/EI
M4 0.285lH
symmetric
6
6
24 x2 /l
606
S10.4

Px1
EA/l 2.723

Py1
0.548

0.548 x1

2.296 y1
The member forces are:

P12
P13
P14
P15
S10.5
0.490W
0.460W
1.428W
0.433W

Pxo
3 / 16

Pyo EA/l 1 / 4

Po
9 / 8
symmetric
3
1/ 2
xo

yo

41 / 4 o
The member forces are:

P1 0.00 kips
P2 8.52 kips
P3 11.48 kips
S10.6
The exibility matrix is:

1
3002
2
0
0 R

3002 R
The cable force is:

R 20.5 kips
S10.7
Then:
The horizontal thrust H may be taken as the redundant.

H 11 kips
Chapter 11
S11.1
Wc 2.55PE
S11.2
Wc 3.1PE
S11.3
607
The stiffness matrix is given by

(4 q )
P 2
21
EI/l
P 3
2
2

(6 q34 ) 3
2
wc 1.55PE /l
S11.4

(2q q23 q24 q )
2
P 2
r23
r24
25
21

3
P 3 EI/l
r23
(q34 q23 )
r34
r24
r34
(q24 q34 q45 ) 4
P 4
c21 1.055
Load Factor 2.81
S11.5

P 2
(9 4n)
EI/l

P 3
2 o
Wc 0.455PE
2 o 2

(9 2n) 3

Answers to supplementary problems part 2: Δ Wa δ 2.16 in upward δ δ

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Answers to supplementary problems part 2: Δ Wa δ 2.16 in upward δ δ

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Answers to supplementary

Structural Analysis: In Theory and Practice

M12 138 kip-in

P24 32.66 kips compression

P24 1.07 kips tension

P13 W/(5.407 0.472a2A/I) compression

P34 11 kips compression

P12 132 kips tension

M12 47.5 kip-ft