sm7 71

________________________________________________________________________
PROBLEM (7.71) Consider the cantilever beam of a triangular cross section subjected to a
variable load w = kx3 kN/m, as shown in Fig. P7.71. Determine:
(a) The maximum bending stress in the beam.
(b) The maximum shearing stress at the neutral axis of the beam.
SOLUTION
44
32.25 .
36
I
in==
5
4
53
max 00
(2 ) 312.5
2
Bx
VV xdx lb== ==
∫
5
45
55
max 00 0
210
B
x
x
MM Vdx dx== = =
∫∫
.37505.312 inlbftlb
⋅
=⋅=
(a) max 3750(2) 3.33
2.25
Mc ksi
I
σ == =
(b) 3
2
1.334.1)667.0)(22( inQ =×=
312.5(1.334) 92.6
2.25(2)
zVQ
p
si
Ib
τ == =
MB
y
5 ft
x
3
250 (5)
lb/ft
2k=
k=
B
R
y
250
w=kx3
1 in.
2 in.
z
0.667 in.=
y
3 in.
2 in.
A
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