Civil Engineering Reference
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stress and in the direction perpendicular to both stresses. Determine also the max-
imum shear strain in the plane of the stresses, the maximum shear stress and their
directions. Take
E
200 000N
/
mm
2
and
ν
=
=
0
.
3.
9
.
0N
/
mm
2
10
−
4
,2
.
01
10
−
4
,
10
−
4
,
γ
max
10
−
4
,
τ
max
=
Ans.
3
.
18
×
×
−
2
.
22
×
=
1
.
17
×
at 45
◦
to the direction of the given stresses.
P.14.9
A cantilever beam of length 2m has a rectangular cross section 100mm wide
and 200mm deep. The beam is subjected to an axial tensile load,
P
, and a vertically
downward uniformly distributed load of intensity
w
. A rectangular strain gauge rosette
attached to a vertical side of the beam at the built-in end and in the neutral plane of
the beam recorded the following values of strain:
ε
a
=
10
−
6
,
ε
b
=
10
−
6
,
1000
×
100
×
10
−
6
. The arm 'a' of the rosette is aligned with the longitudinal axis of
the beam while the arm 'c' is perpendicular to the longitudinal axis.
ε
c
=−
300
×
Calculate the value of Poisson's ratio, the principal strains at the point and hence the
values of
P
and
w
. Young's modulus,
E
200 000N
/
mm
2
.
=
Ans. P
=
4000 kN
w
=
255
.
3 kN/m.
P.14.10
A beam has a rectangular thin-walled box section 50mm wide by 100mm
deep and has walls 2mm thick. At a particular section the beam carries a bending
moment
M
and a torque
T
. A rectangular strain gauge rosette positioned on the top
horizontal wall of the beam at this section recorded the following values of strain:
ε
a
=
10
−
6
. If the strain gauge 'a' is aligned
with the longitudinal axis of the beam and the strain gauge 'c' is perpendicular to
the longitudinal axis, calculate the values of
M
and
T
. Take
E
10
−
6
,
ε
b
=−
10
−
6
,
ε
c
=−
1000
×
200
×
300
×
200 000N
/
mm
2
and
=
ν
=
0
.
3.
Ans. M
=
3333Nm
T
=
1692 Nm.
P.14.11
The simply supported beam shown in Fig. P.14.11 carries two symmetrically
placed transverse loads,
W
. A rectangular strain gauge rosette positioned at the point
P gave strain readings as follows:
ε
a
=−
10
−
6
.
Also the direct stress at P due to an external axial compressive load is 7 N
/
mm
2
.
Calculate the magnitude of the transverse load. Take
E
10
−
6
,
ε
b
=−
10
−
6
,
ε
c
=
222
×
213
×
45
×
31 000N
/
mm
2
,
ν
=
=
0
.
2.
Ans.
W
=
98
.
1kN
Equal distances
W
W
c
b
P
Centroidal
axis
a
300 mm
P
45
°
150 mm
F
IGURE
P.14.11
