Laminated Beam Problem: Calculate Permissible Load P

________________________________________________________________________
PROBLEM (*7.59) A laminated beam is composed of three glued boards (see Fig. P7.59). Calculate:
(a) The highest permissible value for P.
(b) The corresponding maximum flexure stress in the beam.
Given: An allowable shearing stresses of 120 psi in the glue and 500 psi in the wood.
*SOLUTION
y
z
3 in
1.5 in
1.5 in
4 in
P
4
P
P
3 ft 3 ft
6 ft 6 ft
3
3
V
-
M
(lb⋅ft)
-2P
9P
2
P
P
34
3(7) 85.75 .
12
I
in==
x
x
-3P -3P
(a)
3
.375.1275.25.13 inQ =××=
2 (12.375) 120, 1247
85.75(3)
gVQ P Pl
Ib
τ == = = b
Also,
332500, 3500
2237
wVP Pl
A
τ == = =
×b
Thus, lbPall 1247=
(b) max 9 12(1247)(3.5) 5.497
85.75
Mc ksi
I
σ
×
== =
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