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
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- Fall '11
- Staff
- Rigid Body, M1 motorway, G protein coupled receptors, deflection, Downward Load, rotation ua
-
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