263
1 1 2 2.9000000E+07 0.0000000E+00 1.0000000E+01 2.0000000E+02
2 2 3 2.9000000E+07 0.0000000E+00 1.0000000E+01 2.0000000E+02
DISPLACEMENTS Z-ROTATION
X Y THETA
0.00000E+00 0.00000E+00 – 0.69680E–02
0.95468E+00 0.17130E–02 – 0.19754E–02
ELEMENTS
K NODE(I, K) X-FORCE Y-FORCE Z-MOMENT X-FORCE Y-FORCE
1 1 2 – 0.2760E+04 0.1787E+04 0.7438E–01 0.2760E+04 – 0.1787E+04
Z-MOMENT
1 2 0.3217E+06
2 3 0.1083E+06
5.21 For the slant-legged rigid frame shown in Figure P5–21, size the structure for minimum
weight based on a maximum bending stress of 20 ksi in the horizontal beam elements and a
maximum compressive stress (due to bending and direct axial load) of 15 ksi in the slant–
legged elements. Use the same element size for the two slant-legged elements and the same
element size for the two 10-foot sections of the horizontal element. Assume A36 steel is
used.
264
The two angle members and the outside 10 foot members are also designed as ‘I’ beams. These
members were taken to be W14 22. This size has a thickness of 0.335 inches, a depth of 13.74
inches and a width of 5.00 inches.
5.22 For the rigid building frame shown in Figure P5–22, determine the forces in each element
and calculate the bending stresses. Assume all the vertical elements have A = 10 in.2 and I =
100 in4 and all horizontal elements have A = 15 in.2 and I = 150 in.4. Let E =
Figure P5–22
1**** BEAM ELEMENT STRESSES
ELEMENT CASE P/A P/A+M2/S2 P/A–M2/S2 P/A+M3/S3 P/A–M3/S3 WORST SUM
NO. (MODE)
1 1 1.500E+02 1.500E+02 1.500E+02 1.500E+02 1.500E+02 1.500E+02
1.500E+02 1.500E+02 1.500E+02 4.676E+03 –4.376E+03 4.676E+03
4 1 5.591E+01 5.591E+01 5.591E+01 2.054E+03 –1.942E+03 2.054E+03
5.591E+01 5.591E+01 5.591E+01 3.947E+03 –3.835E+03 3.947E+03
10 1 1.920E–01 1.920E–01 1.920E–01 1.177E+03 –1.177E+03 1.177E+03
1.920E–01 1.920E–01 1.920E–01 6.386E+03 –6.386E+03 6.386E+03
11 1 1.098E–01 1.098E–01 1.098E–01 –8.724E+02 8.726E+02 8.726E+02
1.098E–01 1.098E–01 1.098E–01 8.076E+02 –8.074E+02 8.076E+02
12 1 1.098E–01 1.098E–01 1.098E–01 8.076E+02 –8.074E+02 8.076E+02
5.23
Problem 5-23
NUMBER OF ELEMENTS = 10
NUMBER OF NODES = 6
NODE POINTS
K IFII XC(K) YC(K) ZC(K) FORCE(1, K)
266
ELEMENTS
K NODE (I, K) E(K) G(K) A(K) XI(K)
1 1 3 3.0000000E+07 0.0000000E+00 1.0000000E+01 1.5000000E+02
2 2 4 3.0000000E+07 0.0000000E+00 1.0000000E+01 1.5000000E+02
3 3 5 3.0000000E+07 0.0000000E+00 1.0000000E+01 1.5000000E+02
FORCE(2, K) FORCE(3, K)
0.000000 0.000000
0.000000 0.000000
0.000000 0.000000
NODE DISPLACEMENTS Z-ROTATION
3 0.15236E–01 0.10352E–02 – 0.72478E–04
5 0.20440E–01 0.12193E–02 0.20690E–03
6 0.20082E–01 – 0.11183E–02 – 0.74145E–04
ELEMENTS
K NODE(I, K) X-FORCE Y-FORCE Z-MOMENT X-FORCE Y-FORCE Z-MOMENT
1 1 3 – 0.1725E+04 0.5246E+01 0.2132E+02 0.1725E+04 – 0.5246E+01 0.9230E+03
2 2 4 0.1654E+04 0.2770E+02 0.3793E+02 0.1654E+04 – 0.2770E+02 0.4948E+04
Reactions
267
F2x = –27.7 – 1843 = 1871 lb
5.24
Problem 5.24
NUMBER OF ELEMENTS = 6
NUMBER OF NODES = 6
NODE POINTS
K IFIX XC(K) YC(K) ZC(K) FORCE(1, K) FORCE(2, K) FORCE(3, K)
1 1 1 0 0.000000 0.000000 0.000000 0.000000 0.000000 –67500.000000
2 1 1 0 300.000000 0.000000 0.000000 0.000000 0.000000 0.000000
ELEMENTS
K NODE(I, K) E(K) G(K) A(K) XI(K)
1 1 3 3.0000000E+07 0.0000000E+00 1.5000000E+01 2.0000000E+02
268
NODE DISPLACEMENTS Z-ROTATION
X(in.) Y(in.) THETA
1 0.00000E+00 0.00000E+00 – 0.15591E–01
ELEMENTS
K NODE X-FORCE Y-FORCE Z-MOMENT X-FORCE Y-FORCE Z-MOMENT
(I, K) (lb) (lb) (lb in.) (lb) (lb) (lb in.)
1 1 3 – 0.5400E+04 0.3105E+04 – 0.6750E+05 0.5400E+04 – 0.3105E+04 0.6264E+06
2 3 5 – 0.1253E+04 0.1349E+04 – 0.4968E+04 0.1253E+04 – 0.1349E+04 0.2478E+06
5.25 (a)
269
5.26
270
Solution using Autodesk Simulation
271
5.28
272
5.29
273
Figure P5–29
Displacements/Rotations (degrees) of nodes
5.30
NUMBER OF ELEMENTS = 5
NUMBER OF NODES = 6
NODE POINTS
K IFIX XC(K) YC(K) ZC(K) FORCE(1, K) FORCE(2, K) FORCE(3, K)
1 1 1 1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0 0 0 0.000000 360.000000 0.000000 0.000000 0.000000 0.000000
274
5.32
Problem 5.32
NUMBER OF ELEMENTS = 3
NUMBER OF NODES = 4
NODE POINTS
K IFIX XC(K) YC(K) ZC(K) FORCE(1,K) FORCE(2,K) FORCE(3,K)
1 1 1 1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
ELEMENTS
K NODE(I,K) E(K) G(K) A(K) XI(K)
1 1 2 2.1000000E+11 1.0000000E+00 2.0000000E-02 2.0000000E-04
2 2 3 2.1000000E+11 1.0000000E+00 2.0000000E-02 2.0000000E-04
3 3 4 2.1000000E+11 1.0000000E+00 2.0000000E-02 2.0000000E-04
NODE DISPLACEMENTS Z-ROTATION
X Y THETA
1 0.00000E+00 0.00000E+00 0.00000E+00
2 0.42966E–02 0.71361E–05 – 0.24093E–03
ELEMENTS
K NODE X-FORCE Y-FORCE Z- MOMENT X-FORCE Y-FORCE Z-MOMENT
Reactions
5.33
***** Frame Problem 5.33 ******
NUMBER OF ELEMENTS = 9
NUMBER OF NODES = 8
NODE POINTS
276
ELEMENTS
K NODE E(K) G(K) A(K) XI(K) XJ(K)
(I,K)
1 1 3 2.1000000E+06 0.0000000E+00 9.9999998E–03 9. 9999997E–03 0.0000000E+00
2 2 4 2.1000000E+06 0.0000000E+00 9.9999998E–03 9. 9999997E–03 0.0000000E+00
NODE DISPLACEMENTS Z-ROTATION
X Y THETA
1 0.00000E+00 0.00000E+00 0.00000E+00
2 0.00000E+00 0.00000E+00 0.00000E+00
4 0.13092E–01 –0.40236E–04 –0.27869E–02
6 0.21994E–01 –0.50737E–04 –0.15658E–02
8 0.26376E–01 –0.46314E–04 –0.11140E–02
ELEMENTS
K NODE(I,K) X-FORCE Y-FORCE Z-MOMENT
1 1 3 –0.2112E+02 0.3040E+02 0.7493E+02
2 2 4 0.2112E+02 0.2960E+02 0.7383E+02
5.34
277
NUMBER OF ELEMENTS = 3
NUMBER OF NODES = 4
NODE POINTS
K IFIX XC(K) YC(K) ZC(K) FORCE(1,K) FORCE(2,K) FORCE(3,K)
1 1 1 0 0.000000 0.000000 0.000000 0.000000 0.000000 28583.000000
ELEMENTS
K NODE(I,K) E(K) G(K) A(K) XI(K)
1 1 2 2.1000000E+11 1.0000000E+00 1.0000000E–02 1.0000000E–04
NODE DISPLACEMENTS Z-ROTATION
X Y THETA
1 0.00000E+00 0.00000E+00 0.28583E–02
ELEMENTS
K NODE(I,K) X-FORCE Y-FORCE Z-MOMENT X-FORCE Y-FORCE Z-MOMENT
Element (1)
(1)
1
(1)
1
1
2
2
2
x
y
x
y
f
f
m
f
f
m
0
4900
28580
0
4900
5717
0
24500
28580
0
24500
28580
0N
29400 N
57160 N m
0N
19600 N
– 22860 N m
Element (2)
(2)
2
(2)
2
(2)
2
(2)
3
(2)
3
(2)
3
x
y
x
y
f
f
m
f
f
m
=
0
0
5717
0
0
5717
–
0
– 24500
– 28580
0
– 24500
28580
=
0N
24500 N
22,860 N m
0
24500 N
22860 N m
Element (3)
(3)
3
(3)
3
(3)
3
(3)
4
(3)
4
(3)
4
x
y
x
y
f
f
m
f
f
m
=
0
4900
5717
0
4900
28580
–
0
24500
28580
0
24500
28580
=
0N
19600 N
22860 N m
0N
29400 N
– 57160 N m
279
(1)
1x
F1y = –
(1)
1y
f
= – 29400 N
M1 = –
(1)
1
m
= 0 N m
Node 3
(2)
3x
F3y = –
(2) (1)
33yy
ff
= – 44100 N
M3 = 0 N m
Node 2
(2)
2x
F2y = –
(1) (2)
22yy
ff
= – 44100 N
M2 = 0 N m
Node 4
(3)
3x
F4y = –
(3)
4y
f
= – 29400 N
M4 = –
(3)
4
m
= 0 N m
5.35
280
NUMBER OF ELEMENTS = 12
NUMBER OF NODES = 10
NODE POINTS
K IFIX XC(K) YC(K) ZC(K)
1 1 1 1 0.000000 0.000000 0.000000
2 1 1 1 10.000000 0.000000 0.000000
8 0 0 0 10.000000 14.000000 0.000000
9 0 0 0 0.000000 18.000000 0.000000
10 0 0 0 10.000000 18.000000 0.000000
FORCE(1,K) FORCE(2,K) FORCE(3,K)
0.000000 0.000000 0.000000
12000.000000 0.000000 0.000000
8000.000000 0.000000 0.000000
8000.000000 0.000000 0.000000
4000.000000 0.000000 2800.000000
0.000000 0.000000 0.000000
ELEMENTS
K NODE(1,K) E(K) G(K) A(K) XI(K)
1 1 3 2.1000000E+11 0.00000000E+00 2.0000000E–02 2.0000000E–04
2 3 5 2.1000000E+11 0.00000000E+00 1.5000000E–02 1.5000000E–04
7 6 8 2.1000000E+11 0.00000000E+00 1.0000000E–02 1.0000000E–04
8 8 10 2.1000000E+11 0.00000000E+00 1.0000000E–02 1.0000000E–04
9 3 4 2.1000000E+11 0.00000000E+00 4.0000000E–02 6.0000000E–04
10 5 6 2.1000000E+11 0.00000000E+00 4.0000000E–02 6.0000000E–04
11 7 8 2.1000000E+11 0.00000000E+00 4.0000000E–02 6.0000000E–04
12 9 10 2.1000000E+11 0.00000000E+00 4.0000000E–02 6.0000000E–04
NODE DISPLACEMENTS Z-ROTATION
X Y THETA
1 0.00000E+00 0.00000E+00 0.00000E+00
2 0.00000E+00 0.00000E+00 0.00000E+00
3 0.92499E–02 0.32295E–04 – 0.79668E–03
4 0.92428E–02 – 0.32295E–04 – 0.79610E–03
6 0.13435E–01 – 0.45836E–04 – 0.45347E–03
8 0.16317E–01 – 0.53376E–04 – 0.22138E–03
10 0.17393E–01 – 0.54706E–04 – 0.88782E–04
ELEMENTS
K NODE X-FORCE Y-FORCE Z-MOMENT X-FORCE Y-FORCE Z-MOMENT
(I,K)
1 1 3 – 0.2261E+05 0.1601E+05 0.5360E+05 0.2261E+05 – 0.1601E+05 0.4244E+05
2 3 5 – 0.1066E+05 0.1000E+05 0.1728E+05 0.1066E+05 – 0.1000E+05 0.2272E+05
3 5 7 – 0.3959E+04 0.5969E+04 0.1078E+05 0.3959E+04 – 0.5969E+04 0.1310E+05
8 8 10 0.6981E+03 0.1796E+04 0.2896E+04 – 0.6981E+03 – 0.1796E+04 0.4288E+04
5.36
282
Figure P5–37