2.23 Numerical Examples
39
Fig. 2.20 Stresses in element of a body
Fig. 2.21 Mohr’s stress circle
clockwise on the circle to locate point A
. A 240° counterclockwise rotation locates
point B
(Fig. 2.21).
From the above Mohr’s circle,
σ x = (7 + 21 cos 60
◦
)10
6
= 17.5 × 10
6 N/m
2
σ y = −3.5 × 10
6 N/m
2
τ x y = ±21 × 10
6 sin 60
◦
= ±18.86 × 10
6 N/m
2
Example 2.5 A rectangular bar of metal of cross section 30 mm × 25 mm is subjected
to an axial tensile force of 180 KN. Calculate the normal, shear and resultant stresses
on a plane whose normal has the following direction cosines:
(i) l = m =
1
√
2
and n = 0
(ii) l = m = n =
1
√
3
Solution Let normal stress acting on the cross section is given by σ y .
39
Fig. 2.20 Stresses in element of a body
Fig. 2.21 Mohr’s stress circle
clockwise on the circle to locate point A
. A 240° counterclockwise rotation locates
point B
(Fig. 2.21).
From the above Mohr’s circle,
σ x = (7 + 21 cos 60
◦
)10
6
= 17.5 × 10
6 N/m
2
σ y = −3.5 × 10
6 N/m
2
τ x y = ±21 × 10
6 sin 60
◦
= ±18.86 × 10
6 N/m
2
Example 2.5 A rectangular bar of metal of cross section 30 mm × 25 mm is subjected
to an axial tensile force of 180 KN. Calculate the normal, shear and resultant stresses
on a plane whose normal has the following direction cosines:
(i) l = m =
1
√
2
and n = 0
(ii) l = m = n =
1
√
3
Solution Let normal stress acting on the cross section is given by σ y .