Strenght of Materials

41

According to Euler's column theory, the crippling load for a column length (l) hinged at both ends, is

A. `(pi^2 E I)/(l^2)`
B. `(pi^2 E I)/(4l^2)`
C. `(4pi^2 E I)/(l^2)`
D. `(2pi^2 E I)/(l^2)`

42
When a body is subjected to bi-axial stress i.e. direct stresses (`sigma_x`)and(`sigma_y`) in two mutually perpendicular planes accompanied by a simple shear stress (`tau_(xy)`), then minimum normal stress is
A. `(sigma x + sigma y)/(2) + 1/2 sqrt((sigma_x - sigma_y)^2 + 4 tau _(xy)^2)`
B. `(sigma x + sigma y)/(2) - 1/2 sqrt((sigma_x - sigma_y)^2 + 4 tau _(xy)^2)`
C. `(sigma x - sigma y)/(2) + 1/2 sqrt((sigma_x - sigma_y)^2 + 4 tau _(xy)^2)`
D. `(sigma x - sigma y)/(2) - 1/2 sqrt((sigma_x - sigma_y)^2 + 4 tau _(xy)^2)`

43

The extension of a circular bar tapering uniformly from diameter d1 at one end to diameter d2 at the other end, and subjected to an axial pull of P is given by

A. `deltal = (4PE)/(pi l^2)`
B. `deltal = (4pi l d^2)/(PE)`
C. `deltal = (4pl )/(pi E d_1 d_2)`
D. `deltal = (4plE)/(pi d_1 d_2)`

44
The torque transmitted by a hollow shaft of outer diameter (D) and inner diameter (d) is
A. `pi/4 xx tau ((D^2 - d^2)/(D))`
B. `pi/16 xx tau ((D^3 - d^3)/(D))`
C. `pi/16 xx tau ((D^4 - d^4)/(D))`
D. `pi/32 xx tau ((D^4 - d^4)/(D))`

45

In Mohr's circle, the centre of circle from Y-axis is taken as

A. `(6x - 6y)/(2)`
B. `(6x + 6y)/(2)`
C. `(6x - 6y)/(2) + tau`
D. `(6x + 6y)/(2) + tau`