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

ExERcISES
m11.1 Propped Cantilevers. Determine the roller reaction for
a propped cantilever. In each configuration, the roller reaction can
be determined by the superposition of two cantilever cases: a cantilever
with P and a cantilever with w.
m11.2 Beam on three Supports. Use superposition to determine
one roller reaction for a simply supported beam on three
supports.
FIGURE m11.1 FIGURE m11.2
pRoBLEmS
p11.22 For the beams and loadings shown, assume that EI =
5.0 × 10 4 kN · m 2 is constant for each beam.
(a) For the beam in Figure P11.22a, determine the concentrated
downward force P that will make the total beam deflection at
B equal to zero (i.e., v B = 0).
(b) For the beam in Figure P11.22b, determine the concentrated
moment M that will make the total beam slope at A equal to
zero (i.e., θ A = 0).
p11.23 For the beams and loadings shown, assume that EI =
8.0 × 10 6 kip · in. 2 is constant for each beam.
(a) For the beam in Figure P11.23a, determine the concentrated
downward force P that will make the total beam deflection at
B equal to zero (i.e., v B = 0).
(b) For the beam in Figure P11.23b, determine the concentrated
moment M that will make the total beam slope at A equal to
zero (i.e., θ A = 0).
v
P
105 kN.m
v
P
x
x
A
4 m
B
4 m
C
A B 125 kip .ft
15 ft
FIGURE p11.22a
FIGURE p11.23a
M
v
6 kN/m
M
v
7 kips/ft
x
x
A
B
A
B
C
5 m
8 ft 15 ft
FIGURE p11.22b
FIGURE p11.23b
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