sm7 81

________________________________________________________________________
PROBLEM (*7.81) Given that all
σ
= 9 MPa and all
τ
= l.l MPa, design the cross section of
a rectangular wooden beam loaded as shown in Fig. P7.81.
Assumption: The beam is to be twice as deep as it is wide (h = 2b).
*SOLUTION
kNRRM DDC 5.420)4()2(8015)5.2(2:0 ==+−−=
∑
kNRF Cy 5.39:0 ==
∑
From geometry:
4, 1.875
37.5 42.5
mm
m
xx
x
m
−
==
max 1(42.5)(4 1.875) 45.156
2
M
kN m=−= ⋅
Thus,
max
23
3
62
all M
M
bh b
σ ==
3
63
3
3 45.156 10
9 10 , 196 10
2bm b
−
×
×= =×
3
2
all V
A
τ =
3
63
2
3 42.5 10
1.1 10 , 170 10
22 bm b
−
×
×= =×
The required dimensions are
mmhmmb 392196
=
=
-3
20 kN/m
1.5 m
A
B
x
V, kN
42.5 kN
4 m 2b
1
m
C
D
12
-4.8
39.5 kN
37.5
8
x
15 kN m
b
M
,
kN m
x
m-42.5
2 kN
M
max
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.