**Quiz: Civil EngineeringExam: DFCCILTopic: Solid Mechanics**

**Each question carries 1 markNegative marking: 1/4 markTime: 10 Minutes**

Q1. For which material the Poisson’s ratio is more than unity?

A. Steel

B. Copper

C. Aluminium

D. Cast iron

(a) only A

(b) only B

(c) only C

(d) None of these

Q2. The elongation (mm) in a steel bar having a square cross section of diameter 40 mm × 40 mm is 2.5 mm and is subjected to an axial compressive load of P (kN). If the length of the bar is 4 m and modulus of elasticity is E = 250 GPa. What is the value of P(kN)?

(a) 100

(b) 150

(c) 200

(d) 250

Q3. The magnitude of the normal stresses in the x and y direction is 100 MPa and 20 MPa respectively. both the stresses and tensile in nature. Determine the radius of the Mohr’s circle (mm).

(a) 20

(b) 40

(c) 60

(d) 80

Q4. A simply supported beam of span length l carries a uniformly distributed load of 2.0 kN/m and has a diameter of 75 mm. The maximum value of bending moment produced is 8.5 kN-m. What is the value of span length (m) of the beam?

(a) 5.8

(b) 34

(c) 7

(d) 2

Q5. The polar section modulus of a solid circular shaft of diameter ‘d’ about an axis through its center of gravity is:

(a) π/8 d^3

(b) π/16 d^3

(c) π/32 d^3

(d) π/64 d^3

Q6. Radius of curvature of a stressed beam and modulus of elasticity

(a) are directly proportional

(b) are inversely proportional

(c) are curvilinear related

(d) have unpredictable relationship

Q7. If the maximum value of the bending moment in the simply supported beam is 6.75 kNm and the diameter of the beam is 75 mm. Calculate the maximum value of bending stress (MPa).

(a) 150.5

(b) 160.7

(c) 162.97

(d) 165.05

Q8. A cantilever beam is deflected by due to load P if load is doubled, then deflection compared to earlier case will be changed by a factor of:

(a) 2

(b) 1/2

(c) 1/8

(d) 8

Q9. The longitudinal stress in a thin (thickness) cylinder pressure vessel of diameter d and internal pressure, p is

(a) pd/t

(b) pd/2t

(c) pd/4t

(d) pd/8t

Q10. Rankine’s theory is valid to

(a) long column

(b) short column

(c) both

(d) None of the above

Solutions

S1. Ans.(d)

Sol. There is no material whose Poisson’s ratio is more than unity because maximum value of Poisson’s ratio for any material is equal or less than to 0.5.

S2. Ans.(d)

Sol. Given

A = 40 × 40 mm², L = 4 m. δl = 2.5 mm

E = 250 GPa

δl=PL/AE

P=(δl.A.E)/l

P=(2.5×10^(-3)×40×40×10^(-6)×250×10^9)/4

P=250 kN

S3. Ans.(b)

Sol. Given that,

σ_x=100 MPa

σ_y=20 MPa

Radius of Mohr’s circle

R=√(((σ_x-σ_y)/2)+τ_xy^2 )

R=√(((100-20)/2)^2+0^2 )

R=√((40)^2 )

R=40 mm

S4. Ans.(a)

Sol. Maximum bending moment for simply supported in case of UDL.

(WL^2)/8=8.5 KNm

L=√((8.5×10^3×8)/(2×10^3 ))

L = 5.83 m

S5. Ans.(b)

Sol. Polar section modulus

Z_(z-z)=J/y

Z_(z-z)=(π/32 d^4)/(d/2)

Z_(z-z)=π/16 d^3

Where J –Polar moment of inertia

=π/32 d^4

S6. Ans.(a)

Sol. Bending equation

M/I=σ/y=E/R

M/I=E/R

R=EI/M

▭(R α E)

S7. Ans.(c)

Sol. Maximum bending stress (σ_d ) = 32M/(πd^3 )=(32×6.75×10^6)/(π×75^3)

=162.97 MPa

S8. Ans.(a)

Sol. deflection when cantilever beam is subjected to load P

δ_1=(PL^3)/3EI

deflection when load is doubled,

δ_2=((2P) L^3)/3EI

δ_2=2δ_1

S9. Ans.(c)

Sol. In a thin cylindrical pressure vessel,

Longitudinal stress (σ_l )=Pd\/4t

Circumferential (Hoop) stress, (σ_h )=Pd\/2t

S10. Ans.(c)

Sol. Euler’s formula is valid for long columns, while Rankine’s theory is valid for short, medium and long, all types of column.