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FIGURE P3.12
Bar system.
Answer:
1
PR
3
4
EI
PR
3
PR
2
4
EI
PR
2
JG
=
π
JG
(
3
π
−
8
)
=−
π
−
4
V
a
horizontal
+
,
φ
+
a
4
3.15 A concentrated load
P
is applied at the free end of a cantilevered beam. The cross-
section of the beam is a rectangle of height
h
. The stress-strain relation is
k
√
|
|
σ
=
sgn
, where
k
is a constant and
sgn
(read “signum
”)isdefined as
+
1if
>
0
,
−
1if
<
0, and 0 if
=
0. Find the deflection of the free end of the beam under the applied
load.
Answer:
25
P
2
L
4
2
b
2
k
2
h
5
/(
)
Unit Load Method
3.16 Find the displacement of point
a
of the truss shown.
728
PL
AE
3.17 Assume a beam of length
L
is pinned on the left end and fixed on t
he
right end.
Compute the reactions at the fixed end if the beam is loaded with forces
P
at
x
096
PL
Answer:
V
x
=−
0
.
AE
,
z
=
0
.
=
L
/
3
and
x
=
2
L
/
3, where
x
is measured from the left end.
3
3.18 Find the deflection of the free end of the beam of Fig. 3.10c if
L
Answer:
R
=
4
P
/
3,
M
=
PL
/
=
0
.
5m,
p
0
=
1 kN/m,
84 GN/m
2
,I
beam1
10 000 cm
4
,
I
beam2
33 750 cm
4
, and
a
1
E
=
75
.
=
=
=
0
.
2m.
Answer:
4.0857 mm
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