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

p11.24–p11.26 For the beams and loadings shown in Figures
P11.24–P11.26, derive an expression for the reactions at supports A
and B. Assume that EI is constant for the beam.
M 0
v
x
v
w 0
A
L
B
L
C
FIGURE p11.28
x
A
FIGURE p11.24
L
B
v
w
x
v
w
A
L
FIGURE p11.29
B
2L
C
x
L—
2
A
FIGURE p11.25
L
B
v
P
P
x
v
P
A
L L L L
B
C
A
FIGURE p11.26
L
p11.27 For the beam and loading shown in Figure P11.27, derive
an expression for the reactions at supports A and C. Assume
that EI is constant for the beam.
v
A
w
L
FIGURE p11.27
B
p11.28–p11.30 For the beams and loadings shown in Figures
P11.28–P11.30, derive an expression for the reaction force at B.
Assume that EI is constant for the beam. (Reminder: The roller
symbol implies that both upward and downward displacements are
restrained.)
L
L
B
C
x
x
FIGURE p11.30
p11.31 The beam shown in Figure P11.31 consists of a W360 × 79
structural steel wide-flange shape [E = 200 GPa; I = 225 × 10 6 mm 4 ].
For the loading shown, determine
(a) the reactions at A, B, and C.
(b) the magnitude of the maximum bending stress in the beam.
v
v
180 kN.m
FIGURE p11.31
90 kN/m
A B C
3 m 6 m
p11.32 The beam shown in Figure P11.32 consists of a W610 × 140
structural steel wide-flange shape [E = 200 GPa; I = 1,120 × 10 6 mm 4 ].
For the loading shown, determine
(a) the reactions at A, B, and D.
(b) the magnitude of the maximum bending stress in the beam.
x
474