A plate with an elliptical hole in the centre, with semi-major axis (a) perpendicular to the direction of loading and semi-minor axis (b) along the direction of loading, is subjected to a pull P. The maximum stress induced at the edge of the hole is equal to (where $$\sigma $$ = Stress for a plate with no hole i.e. nominal stress)

Rock mass parameters for a shale rock, m_b, s, and a of the Hoek and Brown failure criterion as given in the equation are 2.4, 0.01 and 0.52 respectively. The uni-axial compressive strength (σ_Ci) of intact sh!le is 50 MPa.
$${\sigma _1} = {\sigma _3} + {\sigma _{ci}}{\left( {{m_b}\frac{{{\sigma _3}}}{{{\sigma _{ci}}}} + S} \right)^a}$$
The global rock mass strength of shale in MPa is

A

1.2

B

10.29

C

20.83

D

50,00

When a body is subjected to biaxial stress i.e. direct stresses $$\left( {{\sigma _{\text{x}}}} \right)$$ and $$\left( {{\sigma _{\text{y}}}} \right)$$ in two mutually perpendicular planes accompanied by a simple shear stress $$\left( {{\tau _{{\text{xy}}}}} \right),$$ then maximum normal stress is

A

$$\frac{{{\sigma _{\text{x}}} + {\sigma _{\text{y}}}}}{2} + \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

B

$$\frac{{{\sigma _{\text{x}}} + {\sigma _{\text{y}}}}}{2} - \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

C

$$\frac{{{\sigma _{\text{x}}} - {\sigma _{\text{y}}}}}{2} + \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

D

$$\frac{{{\sigma _{\text{x}}} - {\sigma _{\text{y}}}}}{2} - \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

When a body is subjected to biaxial stress i.e. direct stresses ($${\sigma _{\text{x}}}$$) and ($${\sigma _{\text{y}}}$$) in two mutually perpendicular planes accompanied by a simple shear stress ($${\tau _{{\text{xy}}}}$$ ), then maximum shear stress is

A

$$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

B

$$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

C

$$\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$

D

$$\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$

Given are the steps to draw a perpendicular to a line at a point within the line when the point is near the centre of line. Arrange the steps. Let AB be the line and P be the point in it i. Join F and P which is perpendicular to AB. ii. Now C as centre take the same radius and cut the arc at D and again D as centre with same radius cut the arc further at E. iii. With centre as P take any radius and draw an arc (more than a semicircle) cuts AB at C. iv. Now D, E as centre take radius (more than half of DE) draw arcs which cut at F.

A

i, iv, ii, iii

B

iii, ii, iv, i

C

iv, iii, i, ii

D

ii, i, iv, iii

When a body is subjected to biaxial stress i.e. direct stresses $$\left( {{\sigma _{\text{x}}}} \right)$$ and $$\left( {{\sigma _{\text{y}}}} \right)$$ in two mutually perpendicular planes accompanied by a simple shear stress $$\left( {{\tau _{{\text{xy}}}}} \right),$$ then minimum normal stress is

A

$$\frac{{{\sigma _{\text{x}}} + {\sigma _{\text{y}}}}}{2} + \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

B

$$\frac{{{\sigma _{\text{x}}} + {\sigma _{\text{y}}}}}{2} - \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

C

$$\frac{{{\sigma _{\text{x}}} - {\sigma _{\text{y}}}}}{2} + \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

D

$$\frac{{{\sigma _{\text{x}}} - {\sigma _{\text{y}}}}}{2} - \frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

In order to avoid tearing of the plate at an edge, the distance from the centre line of the rivet hole to the nearest edge of the plate should be equal to (where d = Diameter of rivet hole)

A

1 d

B

1.5 d

C

2.5 d

D

2 d

A flat plate 30mm wide and “t”mm wide is subjected to a tensile force of 5kN. The plate has a circular hole of diameter 15mm with the centre coinciding with the diagonal intersection point of the rectangle. If stress concentration factor=2.16, find the thickness of the plate if maximum allowable tensile stress is 80N/mm².

A

8mm

B

9mm

C

10mm

D

12mm

Steps are given to draw an ellipse by trammel method. Arrange the steps. i. Place the trammel so that R is on the minor axis CD and Q on the major axis AB. Then P will be on the ellipse. ii. Draw two axes AB and CD intersecting each other at O. iii. By moving the trammel to new positions, always keeping R on CD and Q on AB, obtain other points and join those to get an ellipse. iv. Along the edge of a strip of paper which may be used as a trammel, mark PQ equal to half the minor axis and PR equal to half of major axis.

A

i, ii, iii, iv

B

ii, iv, i, iii

C

iii, iv, i, ii

D

iv, i, ii, iii

Which of the following statements are true about edge dislocations?
P. Edge dislocations do not have an extra half plane associated with them.
Q. The Burger vectors is perpendicular to the direction.
R. Edge dislocations can avoid obstacles by cross-slip.
S. Depending on geometry, parallel edge dislocations of opposite signs can attract or repel one another.

A

R

B

P, Q, S

C

Q, S

D

Q, R

To avoid the tearing off the plate of an edge, the margin (i.e., the minimum distance from the centre of the rivet hole to the nearest edge of the plate) should be equal to

A

0.5 d

B

D

C

1.5 d

D

2.5 d