## GATE ME solved questions on stress and strain (Strength of Materials)

**Question #1**

A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s moduli for the sections AB and BC are 3E and E, respectively.

**[GATE 2016 Set 1, 2 marks]**

For the deflection at C to be zero, the ratio P/F is ____________

**Question #2**

A hypothetical engineering stress-strain curve shown in the figure has three straight lines PQ, QR, RS with coordinates P(0,0), Q(0.2,100), R(0.6,140) and S(0.8,130). ‘Q’ is the yield point, ‘R’ is the UTS point and ‘S’ the fracture point.

The toughness of the material (in MJ/m^{3}) is __________

**[GATE 2016 Set 1, 2 marks]**

**Question #3**

In the figure, the load P = 1 N, length L = 1 m, Young’s modulus E = 70 GPa, and the cross-section of the links is a square with dimension 10 mm × 10 mm. All joints are pin joints.

The stress (in Pa) in the link AB is ___________

(Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

**[GATE 2016 Set 2, 2 marks]**

**Question #4**

A circular metallic rod of length 250 mm is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left side and there is a gap of 0.2 mm between the rod and the wall on the right side. If the temperature of the rod is increased by 200^{o} C, the axial stress developed in the rod is __________ MPa.

Young’s modulus of the material of the rod is 200 GPa and the coefficient of thermal expansion is 10^{−5} per ^{o} C.

**[GATE 2016 Set 2, 2 marks]**

**Question #5**

A square plate of dimension L × L is subjected to a uniform pressure load p = 250 MPa on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus E = 200 GPa.

The deformed shape is a square of dimension 𝐿 − 2 𝛿. If 𝐿 = 2 m and 𝛿 = 0.001 m, the Poisson’s ratio of the plate material is __________

**[GATE 2016 Set 3, 2 marks]**

**Question #6**

A rod is subjected to a uni-axial load within linear elastic limit. When the change in the stress is 200 MPa, the change in the strain is 0.001. If the Poisson’s ratio of the rod is 0.3, the modulus of rigidity (in GPa) is ________________

**[GATE 2015 Set 2, 2 marks]**

**Question #7**

A circular rod of length ‘L’ and area of cross-section ‘A’ has a modulus of elasticity ‘E’ and coefficient of thermal expansion ‘α’. One end of the rod is fixed and other end is free. If the temperature of the rod is increased by ΔT, then

(A) stress developed in the rod is E α ΔT and strain developed in the rod is α ΔT

(B) both stress and strain developed in the rod are zero

(C) stress developed in the rod is zero and strain developed in the rod is α ΔT

(D) stress developed in the rod is E α ΔT and strain developed in the rod is zero

**[GATE 2014 Set 1, 1 marks]**

**Question #8**

A metallic rod of 500mm length and 50 mm diameter. when subjected to a tensile force of 100 kN at the ends, experiences an increase in its length by 0.5mm and a reduction in its diameter by 0.015mm.The Poisson’s ratio of the rod material is __________-

**[GATE 2014 Set 1, 1 marks]**

**Question #9**

A steel cube, with all faces free to deform, has Young’s modulus, E, Poisson’s ratio, ν, and coefficient of thermal expansion, α. The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, ΔT, is given by

**[GATE 2014 Set 2, 1 marks]**

(A)0

(B)$\frac{\alpha (\Delta T)E}{1-2\nu }$

(C)$-\frac{\alpha (\Delta T)E}{1-2\nu }$

(D)$\frac{\alpha (\Delta T)E}{3(1-2\nu) }$

**Question #10**

The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option

referring to both figure and table.

**[GATE 14 S3, 1 mark]**

Point on the graph |
Description of the point |

P | 1.Upper yield Point |

Q | 2.ultimateTensile stress |

R | 3.ProProportionalitymir |

S | 4.Elastic Limit |

T | 5.Lower Yield Point |

U | 6.Failure |

(A) P-1, Q-2, R-3, S-4, T-5, U-6

(B) P-3, Q-1, R-4, S-2, T-6, U-5

(C) P-3, Q-4, R-1, S-5, T-2, U-6

(D) P-4, Q-1, R-5, S-2, T-3, U-6

**Question #11**

If the Poisson’s ratio of an elastic material is 0.4, the ratio of modulus of rigidity to Young’s modulus is ______

**[GATE 2014 Set 4, 1 mark]**

**Question #12**

A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in

the figure below. If the Young’s modulus of the material varies linearly from E_{1} to E_{2} along the length of the rod, the normal stress developed at the section-SS is

(A) $\frac{P}{A}$

(B) $\frac{P(E_1-E_2)}{A(E_1+E_2)}$

(C) $\frac{PE_2}{AE_1}$

(D) $\frac{PE_1}{AE_2}$

**[GATE 2013, 1 mark]**

**Question #13**

A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $\Delta T$. If the thermal coefficient of the material is $\alpha$, Young’s modulus is E and the Poisson’s ratio is $\nu$ , the thermal stress developed in the cube due to heating is

(A) $-\frac{\alpha(\DeltaT)E}{(1-2\nu)}$

(B) $-\frac{2\alpha(\DeltaT)E}{(1-2\nu)}$

(C) $-\frac{3\alpha(\DeltaT)E}{(1-2\nu)}$

(D) $-\frac{\alpha(\DeltaT)E}{3(1-2\nu)}$

**[GATE 2012, 2 marks]**

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