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Unformatted text preview: 05Ch05.qxd 9/24/08 4:59 AM Page 409 SECTION 5.5 Normal Stresses in Beams Problem 5.5-23 A small dam of height h 6 ft is constructed of
vertical wood beams AB, as shown in the figure. The wood beams,
which have thickness t 2.5 in., are simply supported by horizontal
steel beams at A and B.
Construct a graph showing the maximum bending stress smax in
the wood beams versus the depth d of the water above the lower
support at B. Plot the stress smax (psi) as the ordinate and the
depth d (ft) as the abscissa. (Note: The weight density g of water
equals 62.4 lb/ft3.) Steel beam
A Wood beam
Wood beam Steel beam h
B Side view Solution 5.5-23 Vertical wood beam in a dam
h 2.5 in. g MAXIMUM BENDING STRESS
Section modulus: S
6 6 ft t 62.4 lb/ft3 smax Let b
width of beam
(perpendicular to the
load at depth d
q0 gbd q0
3L A 3L h 6 ft
A 3L d
L smax gd3
t2 a1 6 q0d2
bt2 6 d) d
3L A 3L d
3L A 3L (62.4)d3
(2.5)2 a1 0.1849d3(54 d RA(L Mmax
g bd ; SUBSTITUTE NUMERICAL VALUES:
d depth of water (ft) (Max. d h 6 ft)
L h 6 ft g 62.4 lb/ ft3 t 2.5 in.
smax psi ANALYSIS OF BEAM Mmax Top view q0d2
9 A 18 9d + d 12d )
830 ; 409 ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.
- Fall '11