Unformatted text preview: 05Ch05.qxd 450 9/25/08 2:29 PM Page 450 CHAPTER 5 Stresses in Beams (Basic Topics) (b) ALLOWABLE LOAD P BASED UPON SHEAR STRESS
V 0.8 MPa t qL
2 (181.44 N/m)(1.2 m)
+ 108.86 (N)
(33,600 mm2)(0.8 MPa)
3 Equate values of V and solve for P: or P 17,920 P 35.6 kN 35,622 N ; NOTE: The shear stress governs and
Pallow 35.6 kN 17,920 N Problem 5.8-11 A square wood platform, 8 ft * 8 ft in area,
rests on masonry walls (see figure). The deck of the platform is
constructed of 2 in. nominal thickness tongue-and-groove planks
(actual thickness 1.5 in.; see Appendix F) supported on two
8-ft long beams. The beams have 4 in. * 6 in. nominal
dimensions (actual dimensions 3.5 in. * 5.5 in.).
The planks are designed to support a uniformly distributed
load w (lb/ft2) acting over the entire top surface of the platform.
The allowable bending stress for the planks is 2400 psi and
the allowable shear stress is 100 psi. When analyzing the
planks, disregard their weights and assume that their reactions
are uniformly distributed over the top surfaces of the supporting
(a) Determine the allowable platform load w1 (lb/ft2) based
upon the bending stress in the planks.
(b) Determine the allowable platform load w2 (lb/ft2) based
upon the shear stress in the planks.
(c) Which of the preceding values becomes the allowable
load wallow on the platform?
(Hints: Use care in constructing the loading diagram for the
planks, noting especially that the reactions are distributed loads
instead of concentrated loads. Also, note that the maximum shear
forces occur at the inside faces of the supporting beams.) 8 ft 8 ft ...
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