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

Solve for Reactions
Solve Equation (j) for the reaction force A y :
36wL 3wL
A y = =
384 32
Ans.
Substitute the reaction force A y into Equation (i) to solve for the moment at A:
M
A
2
wL AL 2 2 2 2
y wL 3wL 10wL 5wL
= − = − =− =−
48 2 48 64 384 192
Substitute the reaction force A y into Equation (a) to determine the reaction force C y :
C
wL wL 3wL 13wL
= − A = − =
2 2 32 32
y y
Finally, determine the reaction moment M C from Equation (b):
Ans.
Ans.
2 2 2 2 2 2
wL 10wL 3wL wL 22wL 11wL
MC = MA + AL y − = − + − = − = − Ans.
8 384 32 8 384 192
pRoBLEmS
p11.1 A beam is loaded and supported as shown in Figure P11.1.
Use the double-integration method to determine the magnitude of
the moment M 0 required to make the slope at the left end of the
beam equal to zero.
v
p11.3 A beam is loaded and supported as shown in Figure P11.3.
(a) Use the double-integration method to determine the reactions
at supports A and B.
(b) Draw the shear-force and bending-moment diagrams for the
beam.
M 0
w
v
A
FIGURE p11.1
L
p11.2 When the load P is applied to the right end of the cantilever
beam shown in Figure P11.2, the deflection at the right end of
the beam is zero. Use the double-integration method to determine
the magnitude of the load P.
B
x
A
FIGURE p11.3
w
L
p11.4 A beam is loaded and supported as shown in Figure P11.4.
Use the double-integration method to determine the reactions at
supports A and B.
B
x
v
w
v
w 0
A
L
P
B
x
A
L
B
x
FIGURE p11.2
FIGURE p11.4
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