Simple Stress and Strain · Strength of Materials · GATE ME

Which one of the following is the definition of ultimate tensile strength (UTS) obtained from a stress-strain test on a metal specimen?

A steel bar is held by two fixed supports as shown in the figure and is subjected to an increases of temperature $$\Delta T = {100^ \circ }C.$$ If the coefficient of thermal expansion and Young's modulus of elasticity of steel are $$11 \times {10^{ - 6}}/{}^ \circ C$$ and $$200$$GPa, respectively, the magnitude of thermal stress (in MPa) induced in the bar is __________.

In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength $$(UTS)$$ refers to

The Poisson's ratio for a perfectly incompressible linear elastic material is

A rod is subjected to an uniaxial 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 ________ .

If the Poisson's ratio of an elastic material is $$0.4$$, the ratio of modulus of rigidity to Young's modulus is _____ .

The number of independent elastic constants required to define the stress-strain relationship for an isotropic elastic solid is ________

A steel cube, with all faces free to deform, has Young’s modulus, $$E,$$ Poisson’s ratio, $$ν,$$ and coefficient of thermal expansion, $$\alpha .$$ The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, $$\Delta T,$$ is given by

The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table

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

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

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 $$\Delta T.$$ then

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 steel rod of length $$L$$ and diameter $$D$$, fixed at both ends, is uniformly heated to a temperature rise of $$\Delta T.$$ The Young's modulus is $$E$$ and the coefficient of linear expansion is $$'\alpha '\,.$$ The thermal stress in the rod is

A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surface. The rod is heated uniformly. If the radial and longitudinal thermal stresses are represented by $${\sigma _r}$$ and $${\sigma _z}$$ respectively, then

In terms of Poisson's ratio $$\left( \mu \right)$$ the ratio of Young's Modulus $$(E)$$ to Shear Modulus $$(G)$$ of elastic materials is

Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having he modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?

A free bar of length 1 m is uniformly heated from $${0^ \circ }C$$ to a temperature of $${t^ \circ }C$$. $$\alpha $$ is the coefficient if linear expansion and $$E$$ the modulus of elasticity. The stress in the bar is

A large uniform plate containing a rivet-hole is subjected to uniform uniaxial tension of 95 MPa. The maximum stress in the plate is

Cylindrical bars P and Q have identical lengths and radii, but are composed of different linear elastic materials. The Young’s modulus and coefficient of thermal expansion of Q are twice the corresponding values of P. Assume the bars to be perfectly bonded at the interface, and their weights to be negligible.

The bars are held between rigid supports as shown in the figure and the temperature is raised by Δ𝑇. Assume that the stress in each bar is homogeneous and uniaxial. Denote the magnitudes of stress in P and Q by σ1 and σ2, respectively.

Which of the statement(s) given is/are CORRECT?

Ignoring the small elastic region, the true stress (𝜎) – true strain (𝜀) variation of a material beyond yielding follows the equation 𝜎 = 400𝜀^0.3 MPa. The engineering ultimate tensile strength value of this material is ________ MPa.

(Rounded off to one decimal place)

A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100 mm². Its elastic modulus varies along its length as given by E(x) = 100 e^-x GPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.

A point mass of $$100$$ kg is dropped onto a massless elastic bar (cross-sectional area = $$100$$ $$mm$$² ,length = $$1$$ m, Young's modulus = $$100$$ GPa) from a height $$H$$ of $$10$$ $$mm$$ as shown (Figure is not to scale). If g = $$10$$ $$m/s$$² , the maximum compression of the elastic bar is _______ $$mm.$$

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^oC, 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 ^oC.

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 $$ \times $$ 10 mm. All joints are pin joints.

The stress (in Pa) in the link AB is _______.

$$(Indicate\,\,compressive\,\,stress\,\,by\,\,a\,\,negative\,$$
$$\,sign\,\,and\,\,tensile\,\,stress\,\,by\,\,a\,\,positive\,\,sign)$$

A square plate of dimension L $$ \times $$ 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$$\delta .$$ If 𝐿 = 2 m and $$\delta $$ = 0.001 m, the Poisson’s ratio of the plate material is __________ .

A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s modules for the sections AB and BC are 3E and E, respectively.
For the deflection at C to be zero, the ratio P/F is ________.

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 tougness of the material (in MJ/m³) is __________.

A $$200$$ mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by $$250$$^oC. If the Young's modulus and coefficient of thermal expansion are $$200$$ GPa and $$1 \times {10^{ - 5}}/{}^ \circ C,$$ respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod is _________

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 $$\upsilon $$, the thermal stress developed in the cube due to heating is

A bar having a cross-sectional area of 700 mm² is subjected to axial loads at the positions indicated. The value of stress in the segment BC is

A steel bar of 40 mm × 40 mm square cross-section is subjected to an axial compressive load of 200 kN. If the length of the bar is 2m and E = 200 GPa. The decrement in length of the bar will be

The figure below shows a steel rod of $$25$$ mm² cross sectional area. It is loaded at four points, K, L, M and N. Assume E_steel $$=$$ $$200$$ GPa. The total change in length of the rod due to loading is

A $$200 \times 100 \times 50$$ mm steel block is subjected to a hydrostatic pressure of $$15$$ MPa. The Young's modulus and Poisson's ratio of the material are 200 GPa and $$0.3$$ respectively. The change in the volume of the block in mm³ is

Below Fig. shows a rigid bar hinged at A and supported in a horizontal position by two vertical identical steel wires. Neglect the weight of the beam. The tension $${T_1}$$ and $${T_2}$$ induced in these wires by a vertical load P applied as shown are

Determine the temperature rise necessary to induce buckling in a 1 m long circular rod of diameter 40 mm shown in the figure below. Assume the rod to be pinned at its ends and the coefficient of thermal expansion as 20 $$ \times $$ 10^-6/^oC. Assume uniform heating of the bar.