Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

55 kip·ft
30 kips
2.5 kips/ft
30 kips
6 ft 2 ft
4 kips
1 kips/ft
15 kips
From these equilibrium equations, the beam reactions
at pin support A and roller support C are
A
y
= 31.42 kips and C = 47.58 kips
y
A y
A
B
5 ft 7 ft
4 ft
C y
C
D
Shear-Force and Bending-Moment Diagrams
The shear-force and bending-moment diagrams for the
beam and loading are shown. The maximum internal
bending moment in the beam is M = 70.83 kip · ft, and
it occurs at B.
55 kip·ft
30 kips
2.5 kips/ft
1 kip/ft
15 kips
Required Section Modulus
The flexure formula can be solved for the minimum
section modulus required to support the maximum internal
bending moment without exceeding the 30 ksi
allowable bending stress:
A
31.42 kips
V
M
–55.00 kip·ft
B
5 ft 7 ft
4 ft
31.42 kips 47.58 kips
–11.08 kips
70.83 kip·ft
18.92 kips
C
19.00 kips
–28.58 kips
–68.00 kip·ft
D
15.00 kips
σ
max
M
= ≤ σ
S
allow
M (70.83 kip⋅ft)(12in./ft)
∴ S ≥ =
σ allow 30 ksi
3
= 28.33 in.
(a) Select acceptable steel shapes: The properties of
selected standard steel wide-flange shapes are presented
in Appendix B. W shapes having a section
modulus greater than or equal to 28.33 in. 3 are acceptable
for the beam and loading considered here. Since
the cost of a steel beam is proportional to its weight,
it is generally preferable to select the lightest acceptable
shape for use.
Follow the procedure for selecting standard steel
shapes presented in Table 8.1. By this process, the
following shapes are identified as being acceptable
for the beam and loading:
W8 × 40, S = 35.5 in. 3
W10 × 30, S = 32.4 in. 3
W12 × 26, S = 33.4 in. 3
W14 × 22, S = 29.0 in. 3
W16 × 31, S = 47.2 in. 3
W18 × 35, S = 57.6 in. 3
(b) Select the most economical W-shape: The most economical W shape can now be
selected from the short list of acceptable shapes. From this list, a W14 × 22 standard
steel wide-flange shape is identified as the lightest-weight section for this beam and
loading.
Ans.
268