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

56 mm
y
13.5 mm 8.5 mm (3) K (4)
z
(5)
7 mm
5 mm
3 mm
42 mm
Calculating Q at point K: The area to be considered in the calculation of Q
at point K is highlighted in the cross section. At point K, Q is the moment
of areas (3), (4), and (5) about the z centroidal axis:
Q
K
= 2[(3 mm)(7 mm)(8.5 mm)]
+ (56 mm)(3 mm)(13.5 mm) = 2,625 mm
3
3 mm 20 mm 3 mm
56 mm
y
3 mm
The shear stress acting at K is
3
VQK
(2,000 N)(2,625 mm )
τ K = = = 9.92 MPa Ans.
4
It (88,200 mm )(6 mm)
z
(c) Maximum Horizontal Shear Stress
The maximum value of Q corresponds to an area that begins at, and extends
away from, the neutral axis. For this location, however, the words extends
away from the neutral axis can mean either the area above or the area below
the neutral axis. The value obtained for Q is the same in either case. For the
double-tee cross section, the calculation of Q is somewhat simpler if we
consider the highlighted area below the neutral axis. In that case,
30 mm
z
(6) (7)
3 mm 20 mm 3 mm
15 mm
42 mm
Q = 2[(3 mm)(30 mm)(15 mm)] = 2,700 mm
max
The maximum horizontal shear stress in the double-tee shape is then
3
VQmax
(2,000 N)(2,700 mm )
τ max = = = 10.20 MPa Ans.
4
It (88,200 mm )(6 mm)
z
3
mecmovies
ExAmpLES
m9.4 Determine the shear stress at points H and K for a
simply supported beam that consists of the WT265 × 37
standard steel shape shown.
m9.5 Determine the distribution of shear stresses produced
in a tee shape.
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