Page 222 - Shigley's Mechanical Engineering Design

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Deflection and Stiffness 197
4–20 Like Prob. 4–18, this problem provides another beam to add to Table A–9. For the simply sup-
ported beam shown with an overhanging uniform load, use statics and double integration to
show that
wa 2 wa wa 2
R 1 = R 2 = (2l + a) V AB =− V BC = w(l + a − x)
2l 2l 2l
wa 2 w 2
M AB =− x M BC =− (l + a − x)
2l 2
2
wa x 2 2 w 4 2 4
y AB = (l − x ) y BC =− [(l + a − x) − 4a (l − x)(l + a) − a ]
12EIl 24EI

y
l a
R w
Problem 4–20 1
A B C
x
R 2

4–21 Consider the uniformly loaded simply supported steel beam with an overhang as shown. The
4
second-area moment of the beam is I = 0.05 in . Use superposition (with Table A–9 and the
results of Prob. 4–20) to determine the reactions and the deflection equations of the beam. Plot
the deflections.

w = 100 lbf/in
C
A
Problem 4–21 B
y y
10 in 4 in

4–22 Illustrated is a rectangular steel bar with simple supports at the ends and loaded by a force F at
the middle; the bar is to act as a spring. The ratio of the width to the thickness is to be about
b = 10h, and the desired spring scale is 1800 lbf/in.
(a) Find a set of cross-section dimensions, using preferred fractional sizes from Table A–17.
(b) What deflection would cause a permanent set in the spring if this is estimated to occur at a
normal stress of 60 kpsi?

F
A
b
Problem 4–22
A h
3 ft Section A–A

4–23* to For the steel countershaft specified in the table, find the deflection and slope of the shaft at
4–28* point A. Use superposition with the deflection equations in Table A–9. Assume the bearings con-
stitute simple supports.