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

p10.31 For the beam and loading shown in Figure P10.31, use
discontinuity functions to compute
(a) the slope of the beam at B.
(b) the deflection of the beam at A.
Assume a constant value of EI = 133,000 kip ⋅ ft 2 for the beam.
v
4 kips/ft
p10.34 For the beam and loading shown in Figure P10.34, use
discontinuity functions to compute
(a) the slope of the beam at B.
(b) the deflection of the beam at B.
Assume a constant value of EI = 110,000 kN · m 2 for the beam.
v
15 kN/m
40 kN/m
A
FIGURE p10.31
p10.32 For the beam and loading shown in Figure P10.32, use
discontinuity functions to compute
(a) the slope of the beam at B.
(b) the deflection of the beam at C.
Assume a constant value of EI = 34 × 10 6 lb ⋅ ft 2 for the beam.
v
A
7,000 lb/ft
9 ft 5 ft
p10.33 For the beam and loading shown in Figure P10.33, use
discontinuity functions to compute
(a) the slope of the beam at A.
(b) the deflection of the beam at B.
B
4 ft 9 ft
5 ft
FIGURE p10.32
Assume a constant value of EI = 370,000 kip ⋅ ft 2 for the beam.
v
8 kips/ft
B
C
C
D
x
x
p10.35 For the beam and loading shown in Figure P10.35, use
discontinuity functions to compute
(a) the deflection of the beam at A.
(b) the deflection of the beam at C.
Assume a constant value of EI = 24,000 kN · m 2 for the beam.
v
p10.36 For the beam and loading shown in Figure P10.36, use
discontinuity functions to compute
(a) the slope of the beam at B.
(b) the deflection of the beam at A.
Assume a constant value of EI = 54,000 kN · m 2 for the beam.
v
20 kN/m
A
FIGURE p10.34
35 kN
4 m
A B C
D
2.5 m
25 kN/m
FIGURE p10.35
4.0 m
50 kN/m
70 kN/m
1.5 m
B
x
x
x
x
A B C
A
B
C
12 ft 12 ft
3 m 1 m
FIGURE p10.33
FIGURE p10.36
10.7 Determining Deflections by
the Method of Superposition
The method of superposition is a practical and convenient method for obtaining beam
deflections. The principle of superposition states that the combined effect of several loads
acting simultaneously on an object can be computed from the sum of the effects produced by
each load acting individually. How can this principle be used to compute beam deflections?
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