Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

To determine the average horizontal shear stress in the glue joints at b, c, and d
by the shear stress formula both, the first moment of area, Q, and the width of the
stressed surface, t, must be determined for each location.
12 in.
1.50 in.
z
6 in.
b
5.25 in.
Neutral axis
Shear stress in glue joint b: The portion of the cross section to be considered for
the first moment of area, Q, about the neutral axis begins at point b and extends
away from the neutral axis. The area to be considered for joint b is highlighted
in the accompanying diagram. The area of the highlighted region is
(1.50 in.)(6 in.) = 9 in. 2 . The distance from the neutral axis to the centroid of the
highlighted area is 5.25 in. The first moment of area corresponding to joint b is
calculated as
Q = (1.50 in.)(6 in.)(5.25 in.) = 47.25 in.
b
3
6 in.
The width of the glue joint is t = 6 in. From the shear stress formula, the average
horizontal shear stress in glue joint b is computed as
3
VQb
(4.5 kips)(47.25 in. )
τ b = = = 0.0410 ksi = 41.0 psi Ans.
4
It (864 in. )(6 in.)
z b
6 in.
This shear stress acts in the x direction on the glue joint. (Note: The shear stress
determined by the shear stress formula is an average shear stress because the shear
stress actually varies somewhat in magnitude across the 6 in. width of the cross
section. The variation is more pronounced for cross sections that are relatively
short and wide.)
12 in.
4.50 in.
z
c
3.75 in.
Neutral axis
Shear stress in glue joint c: The area to be considered for joint c, highlighted in the
figure to the left, begins at c and extends away from the neutral axis. The first moment
of area corresponding to joint c is calculated as
Q = (4.50 in.)(6 in.)(3.75 in.) = 101.25 in.
c
The width of the glue joint is t = 6 in. From the shear stress formula, the average
horizontal shear stress acting in the x direction in glue joint c is computed as
3
6 in.
3
VQc
(4.5 kips)(101.25 in. )
τ c = = = 0.0879 ksi = 87.9 psi Ans.
4
It (864 in. )(6 in.)
z c
12 in.
z
Neutral axis
Shear stress in glue joint d: The area to be considered for joint d, highlighted in
the accompanying figure, begins at d and extends away from the neutral axis. In
this instance, however, the area extends downward from d, away from the z axis.
The first moment of area corresponding to joint d is calculated as
3 in.
6 in.
d
4.50 in.
Q = (3 in.)(6 in.)(4.50 in.) = 81.0 in.
d
The average horizontal shear stress acting in the x direction in glue joint d is computed
as
3
VQd
(4.5 kips)(81.0 in. )
τ d = = = 0.0703 ksi = 70.3 psi Ans.
4
It (864 in. )(6 in.)
z d
3
334