sm10 79

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________________________________________________________________________
PROBLEM (10.79) A propped cantilever beam AB supports a uniform load of intensity w over
half-span AC (Fig. P10.79). Determine:
(a) All of the reactions for this beam.
(b) The deflection at C for the given numerical values if w = 10 kN/m, L = 6 m, and EI = 3.44 MN
⋅
m2.
SOLUTION
(a)
0
'''' 2
L
EIv w w x
=− + < − >
1
''' 2
L
EIv wx w x C
=− + < − >+
22
12
1
'' 222
wL
EIv wx x C x C
=− + < − > + +
332
123
11
'6622
wL
EIv wx x C x C x C
=− + < − > + + +
4432
1234
111
24 24 2 6 2
wL
EIv wx x C x C x C x C
=− + < − > + + + +
Using boundary conditions:
43
(0) 0: 0 '(0): 0vCvC== =
22
12
11
''( ) 0 : 0
28
v L wL wL C L C=− + ++=
4432
12
1111
() 0: 0
24 384 6 2
v L wL wL C L C L=− + + + =
Solving,
2
12
57 9
128 128
CwLC wL==−
Thus,
2
57 9
128 128
AA
R
wL M wL=↑=
Then 7
0: 128
yB
FRwL==↑
∑
Continued on next slide
R
A
A
B
y
x
RB
MA
L/
2 C
L/
2
w

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instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
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(b) Equation (a) is therefore
44322
[32 32 57 27 ]
768 2
wL
vxxLxLx
EI
=−+<−>+−
Make x=L/2 in the above
4
13
6144
CwL
vEI
=↓
Substituting the given data
34
6
13 10 10 (6) 7.97
6144 3.44(10 )
C
vmm
×
==↓