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The uni-axial compressive strength and modulus of elasticity of a rock sample are 90 MPa and 30 GPa respectively. The stored strain energy per unit volume in kN.m/m<sup>3</sup> of the sample at the time of failure is
A
1.5
B
140
C
270
D
135
Correct Answer:
135
The uniaxial compressive strength of a limestone sample is 80 MPa. The sample is confined at a pressure of 20 MPa in a triaxial compressive strength test. Based on Hoek-Brown failure criteria the maximum principal stress at failure in MPa is
(Consider rock constants as m = 7.88, s = 1.0 and a = 0.5)
A
117.9
B
132.3
C
137.9
D
157.9
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
A glass reinforced polymer composite comprises of 35 volume % glass fiber and 65 volume % of polymer resin. The elastic moduli of glass and polymer resin are respectively 70 GPa and 3 GPa. The elastic modulus of the composite (in GPa) under iso-strain state is
A
4.51
B
25.45
C
26.45
D
27.45
During uniaxial compressive testing of a rock specimen of diameter 54 mm and length 120 mm, the axial strain was found to be 6.5 × 10
-4
mm/mm. If the Poisson's ratio of the rock is 0.3, the volumetric strain of the rock specimen in mm/mm is
A
1.95 ∗ 10<sup>-4</sup>
B
2.60 ∗ 10<sup>-4</sup>
C
2.34 ∗ 0<sup>-2</sup>
D
3.12 ∗ 10<sup>-2</sup>
A core sample of 54 mm diameter having Young's modulus of 68.97 Gpa fails in uniaxial compression at 0.1% axial strain. The axial load at failure in kN is
A
158.00
B
68.97
C
58.00
D
15.80
From an alloy, two specimens are machined and tested separately under tension and compression. The engineering stress-strain curves as well as the true stress-true strain curves for tension and compression are plotted in the same diagram. Identify the correct statements:
P. The engineering stress-strain curves in tension and compression are identical.
Q. The true stress-true strain curve in compression is lower than the true stresstrue strain curve in tension due to Bauschinger effect.
R. The true stress-true strain curve in tension is above the corresponding engineering stress-strain, curve.
S. The true stress-true strain curve in tension and compression are identical.
A
P, Q
B
Q, R
C
Q, S
D
R, S
Graphite fibres are used to make undirectional Al-matrix composites. Young's modulus of graphite and aluminium are 400 GPa respectively. If a composite contains 60 volume % of fiber and is loaded along the fiber direction, the Youngs Modulus of the composite is . . . . . . . . GPa.
A
60
B
164
C
264
D
364
Elastic failure of a material occurs, when the tensile stress equals yield strength, yield point or the elastic limit. Also, the elastic failure occurs according to maximum strain theory, when the maximum tensile strain equals (where, $$\sigma $$ = yield strength and E = modulus of elasticity)
A
E
B
$$\sigma $$
C
$$\frac{\sigma }{{\text{E}}}$$
D
$$\frac{{\text{E}}}{\sigma }$$
"It is now expected that the variable production cost per unit and the selling price per unit will each increase by 10%, and fixed production cost will rise by 25%. What will be the new break even point?
Selling price - Rs 6 per unit
Variable production cost - Rs 1.20 per unit
Variable selling cost - Rs 0.40 per unit
Fixed production cost - Rs 4 per unit
Fixed selling cost - Rs 0.80 per unit
Budgeted production and sales for the year are 10,000 units."
A
8,788 units
B
11,600 units
C
11,885 units
D
12,397 units
From the stress-strain diagram shown below, the tangent and the secant moduli of elasticity in GPa are
A
4.0, 2.2
B
3.3, 2.3
C
3.3, 1.5
D
4.0, 1.5
