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

p10.5 For the beam and loading shown in Figure P10.5, use the
double-integration method to determine
(a) the equation of the elastic curve for the beam.
(b) the slope at A.
(c) the slope at B.
(d) the deflection at midspan.
Assume that EI is constant for the beam.
p10.8 For the cantilever steel beam [E = 200 GPa; I = 129 ×
10 6 mm 4 ] shown in Figure P10.8, use the double-integration method
to determine the deflection at A. Assume that L = 2.5 m, P = 50 kN,
and w 0 = 90 kN/m.
v
P
w 0
v
M 0
A
FIGURE p10.5
L
p10.6 For the beam and loading shown in Figure P10.6, use the
double-integration method to determine
(a) the equation of the elastic curve for the beam.
(b) the maximum deflection.
(c) the slope at A.
Assume that EI is constant for the beam.
B
x
A
FIGURE p10.8
L
p10.9 For the beam and loading shown in Figure P10.9, use the
double-integration method to determine
(a) the equation of the elastic curve for the cantilever beam.
(b) the deflection at the free end.
(c) the slope at the free end.
Assume that EI is constant for the beam.
v
w 0
B
x
v
w
A
B
x
x
L
A
L
B
FIGURE p10.9
FIGURE p10.6
p10.7 For the simply supported steel beam [E = 200 GPa; I =
129 × 10 6 mm 4 ] shown in Figure P10.7, use the double-integration
method to determine the deflection at B. Assume that L = 4 m, P =
60 kN, and w = 40 kN/m.
p10.10 For the beam and loading shown in Figure P10.10, use
the double-integration method to determine
(a) the equation of the elastic curve for the cantilever beam.
(b) the deflection at B.
(c) the deflection at the free end.
(d) the slope at the free end.
Assume that EI is constant for the beam.
v
P
w
v
w
x
x
A
B
C
A
B
C
FIGURE p10.7
L—
2
L—
2
L—
2
FIGURE p10.10
L—
2
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