455_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

SECTION 5.8 Shear Stresses in Rectangular Beams
449
Solution 5.8-10 Simply supported wood beam
L 1.2 m q g bh 181.44 N/m
g 5.4 kN/m
3
S
bh
2
6
1344 * 10
3
mm
3
A bh 33,600 mm
2
b 140 mm h 240 mm
(a) A
LLOWABLE BASED UPON BENDING STRESS
Equate values of and solve for :
or P 38.0 kN ;
0.3 P + 32.66 11,424 P 37,970 N
P M
max
11,424 N
#
m
M
max
S s
allow
(1344 * 10
3
mm
3
)(8.5 MPa)
( P newtons; M N
#
m)
0.3 P + 32.66 N
#
m
+
(181.44 N/m)(1.2 m)
2
8
M
max
PL
4
+
qL
2
8
P (1.2 m)
4
s
allow
8.5 MPa s
M
max
S
P
From Appendix F: Select in. beam (nominal
dimensions)
(b) R
EPEAT
(
A
)
CONSIDERING THE WEIGHT OF THE BEAM
R
B
7.83 * 10
3
1b
R
B
7.725 * 10
3
1b +
q
beam
L
2
q
beam
20.964
1b
ft
g 35
1b
ft
3
q
beam
g A
A 86.25 in.
2
S 165.3 in.
3
;
8 * 12
s
max
M
S
S
req
M
max
s
allow
S
req
120.6 in.
3
beam is still satisfactory for shear.
beam is still satisfactory for moment.
; Use 8 * 12 in. beam
8 * 12
S
req
M
max
s
allow
S
req
122.3 in.
3
< S
M
max
2.293 * 10
4
1b-ft
M
max
R
B
d
qd
2
2
q
total
q + q
beam
q
total