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Standard XII
Physics
Damped Oscillations
The horizonta...
Question
The horizontal thrust on the ends of a two hinged semicircular arch of radius R carrying
A
A uniformly distributed load w per unit run over its entire span is
(
4
/
3
)
×
(
w
R
/
π
)
.
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B
A uniformly distributed load w per unit run over its right half span is
(
2
/
3
)
×
(
w
R
/
π
)
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C
All option are correct
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D
A distributed load varying from zero at the left end to w per unit horizontal run at the right end is
(
2
/
3
)
×
(
w
R
/
π
)
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Solution
The correct option is
C
All option are correct
Case -1 : UDL throughtout span of arch.
′
y
′
a
t
a
n
y
s
e
c
t
i
o
n
=
R
s
i
n
θ
(A) Reactions at the supports
(i) Vertical support reactions
v
B
=
w
R
,
V
A
=
w
R
(ii) Horizontal thrust
H
=
4
3
w
R
π
(
R
e
m
e
m
b
e
r
)
Case- 2 UDL at half right of span of arch :
(A) Reactions at the support
(i) Vertical support reaction
V
A
=
w
×
R
4
,
V
B
=
3
w
R
4
(ii) Horizontal thrust
Since the arch is symmetrically loaded in previous case thus the horizontal thrust obtain at that case is exactly double compared to this case .
H
=
1
2
×
4
3
w
R
π
=
2
3
w
R
π
(
R
e
m
e
m
b
e
r
)
Case : B uniformly varied load on entired span.
(A) reactions at the supports
(i) Vertical support reaction
V
B
=
2
3
w
R
,
V
A
=
w
R
3
(ii) Horizontal thrust
H
=
2
w
R
3
π
(
R
e
m
e
m
b
e
r
)
Note:
Two hinged arch:
Two hinged arch is statically indeterminate structure of one degree having two hinge support at its end.
Two hinged arch is commonly made of metal & timber.
It is not as rigid as fixed arch, thus it is some what insensitive to settlement.
Usually, horizontal reaction is treated as redundant and is evaluated by the method of least work.
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