________________________________________________________________________
PROBLEM (7.53) As shown in Fig. P7.53, a beam is constructed of four wood boards nailed
together. Two of the boards, measure 20 x I00 mm and two 25 x 100 mm. Calculate:
(a) The shear force in each nail.
(b) The shearing stress 40 mm from the top of the beam.
Given: A longitudinal spacing between each nail of s = 100 mm and an allowable vertical shear force in
the beam of V = 3 kN.
SOLUTION
A
y
1
33
1[100(140) 50(100) ]
12
I=−
64
18.7 10 mm=×
(a) 33
111 101206010020 mmyAQ ×=××==
36
16
3 10 (120 10 ) 19.25
18.7 10
VQ kN m
I
−
−
××
==
×
We have or Fsq 2=⋅
3
1(19.25 10 )(0.1) 962.5
2
FN=× =
(b) )402025(2101202 3
221 ××+×=+= yAQQ
33
10160 mm×=
36
63
3 10 (160 10 ) 513.4
18.7 10 (2 25 10 )
VQ kPa
Ib
τ
−
−−
××
== =
×××
z
40 70
A
2
70
25
25
20
20
100
C
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