758_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

D
EFLECTION
d
AT THE MIDPOINT
C
1
2
a
M
0
2 EI
b a
L
2
b a
L
6
b
M
0
L
2
48 EI
with respect to C
t
C
2
/ A
C
2
C
1
first moment of area between A and C
Distance CC
1
1
2
( BB
1
)
M
0
L
2
12 EI
(These results agree with Case 7 of Table G-2.)
M
0
L
2
16 EI
(Downward) ;
d CC
1
C
2
C
1
M
0
L
2
12 EI
M
0
L
2
48 EI
Problem 9.6-10
The simple beam AB shown in the figure supports two
equal concentrated loads P , one acting downward and the other upward.
Determine the angle of rotation u
A
at the left-hand end, the deflection
d
1
under the downward load, and the deflection d
2
at the midpoint
of the beam.
Solution 9.6-10 Simple beam with two loads
Because the beam is symmetric and the load is
antisymmetric, the deflection at the midpoint is zero.
‹ d
2
0 ;
A
NGLE OF ROTATION
u
A
AT END
A
D
EFLECTION
d
1
UNDER THE DOWNWARD LOAD
Pa
2
( L 2 a )
2
6 LEI