재료역학7판06-03 Chap

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재료역학7판06-03 Chap에 대한 보고서 자료입니다.

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Problem 6.8-3 A beam of wide-flange shape has the cross section
shown in the figure. The dimensions are b
5.25 in., h
7.9 in.,
tw
0.25 in., and tf
0.4 in. The loads on the beam produce a shear
force V
6.0 k at the cross section under consideration.
(a) Using centerline dimensions, calculate the maximum shear
stress in the web of the beam.
(b) Using the more exact analysis of Section 5.10 in Chapter 5,
calculate the maximum shear stress in the web of the beam and
compare it with the stress obtained in part (a).
Solution 6.8-3 Wide-flange beam
SECTION 6.8 Beams with Inclined Loads 403
b
5.25 in. h
7.9 in. tw
0.25 in.
tf
0.4 in. V
6.0 k
(a) CALCULATIONS BASED ON CENTERLINE DIMENSIONS
(SECTION 6.8)
Moment of inertia (Eq. 6-59):
Iz
10.272  65.531
75.803 in.4
Maximum shear stress in the web (Eq. 6-54):

3244 psi
tmax
¢
btf
tw

h
4
≤
Vh
2Iz

(10.375 in.) (312.65 lb
in.3)
Iz

tw h3
12

btf h2
2
(b) CALCULATIONS BASED ON MORE EXACT ANALYSIS
(SECTION 5.10)
See Figure 5-38. Replace h by h2 and t by tw.
h2
h  tf
8.3 in. h1
h  tf
7.5 in.
Moment of inertia (Eq. 5-47):
Maximum shear stress in the web (Eq. 5-48a):

(40.336 lb/in.5)(80.422 in.3)

3244 psi
NOTE: Within the accuracy of the calculations, the
maximum shear stresses are the same.
tmax

V
8Itw
(bh 2
2 bh 1
2 twh 1
2 )
I

1
12
(892.51 in.4)
74.376 in.4
I

1
12
(bh 2
3 bh 1
3 twh 1
3 )
b
z h
y
C
tf
tf
tw
b
z h1 h h2
y
C
tf
tf
tw
Probs. 6.8-3 and 6.8-

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재료,   역학,   재료역학,   재료역학7판06-03 Chap