GATE Mechanical Engineering

The yield stress of a metal in uniaxial tension is 200 MPa . According to von Mises yield criterion, the yield stress (in MPa) of the metal in pure shear is closest to

A metallic square plate is subjected to a uniform hydrostatic pressure $(P)$. Choose the correct Mohr's circle representing the state of stress at any point in the plate from the o...

The phases present in pearlite are

Which of the following beam(s) is/are statically indeterminate?

The principal stresses at a point P in a solid are 70 MPa, −70 MPa and 0. The yield stress of the material is 100 MPa. Which prediction(s) about material failure at P is/are CORREC...

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...

A cylindrical transmission shaft of length 1.5 m and diameter 100 mm is made of a linear elastic material with a shear modulus of 80 GPa. While operating at 500 rpm, the angle of t...

Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following stat...

A thin-walled cylindrical pressure vessel has mean wall thickness of t and nominal radius of r. The Poisson’s ratio of the wall material is 1/3. When it was subjected to some inter...

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

A structural member under loading has a uniform state of plane stress which in usual notations is given by σ x = 3P, σ y = -2P and τ xy = √2 P, where P > 0. The yield strength of t...

Consider a beam with circular cross-section of diameter $$d.$$ The ratio of the second moment of area about the neutral axis to the section modulus of the area is

A motor driving a solid circular steel shaft transmits $$40$$ $$kW$$ of power at $$500$$ $$rpm$$. If the diameter of the shaft is $$40$$ $$mm,$$ the maximum shear stress in the sha...

A rectangular region in a solid is in a state of plane strain. The $$(x,y)$$ coordinates of the corners of the undeformed rectangle are given by $$P(0,0), Q(4,0), R(4,3), S(0,3).$$...

A cantilever beam of length $$L$$ and flexural modulus $$EI$$ is subjected to a point load $$P$$ at the free end. The elastic strain energy stored in the beam due to bending (negle...

A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100 mm 2 . Its elastic modulus varies along its length as given by E(x) = 100 e -x GPa,...

A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa....

For a loaded cantilever beam of uniform cross-section, the bending moment (in N-mm) along the length is M(x) = 5x 2 +10x, where x is the distance (in mm) measured from the free end...

The state of stress at a point is $${\sigma _x} = {\sigma _y} = {\sigma _z} = {\tau _{xz}} = {\tau _{zx}} = {\tau _{yz}} = {\tau _{zy}} = 0$$ and $${\tau _{xy}} = {\tau _{yx}} = 50...

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

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

A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is

A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is

Two circular shafts made of same material, one solid $$(S)$$ and one hollow $$(H)$$, have the same length and polar moment of inertia. Both are subjected to same torque. Here. $${\...

A cantilever beam having square cross-section of side $$a$$ is subjected to an end load. If a is increases by $$19$$%, the tip deflection decreases approximately by

The spring constant of a helical compression spring DOES NOT depend on

In a plane stress condition, the components of stress at a point are $${\sigma _x} = 20$$ MPa, $${\sigma _y} = 80$$ MPa and $${\tau _{xy}} = 40$$ MPa, The maximum shear stress (in...

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 t...

A cylindrical tank with closed ends is filled with compressed air at a pressure of $$500 kP$$a. The inner radius of the tank is $$2 m,$$ and it has wall thickness of $$10 mm.$$ The...

A hollow shaft of $$1$$ m length is designed to transmit a power of $$30$$ kW at $$700$$ rpm. The maximum permissible angle of twist in the shaft is $${1^0}.$$ The inner diameter o...

A rope brake dynamometer attached to the crank shaft of an $$I.C.$$ engine measures a brake power of $$10$$ kW when the speed of rotation of the shaft is $$400$$ rad/s. The shaft t...

A gas is stored in a cylindrical tank of inner radius $$7$$ m and wall thickness $$50$$ mm. The gage pressure of the gas is $$2$$ MPa. The maximum shear stress (in MPa) in the wall...

The deflection of a spring with 20 active turns under a load of 1000 N is 10 mm. The spring is made into two pieces each of 10 active coils and placed in parallel under the same lo...

A hollow shaft (d 0 = $$2$$d i , where d 0 and d i are the outer and inner diameters respectively) needs to transmit $$20$$ kW power at $$3000$$ RMP. If the maximum permissible she...

Consider a steel (Young’s modulus $$E = 200$$ $$GP$$a) column hinged on both sides. Its height is $$1.0$$ $$m$$ and cross-section is $$10 mm$$ $$ \times $$ $$20 mm$$. The lowest Eu...

For the same material and the mass, which of the following configurations of flywheel will have maximum mass moment of inertia about the axis of rotation $$OO’$$ passing through th...

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 reduc...

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 reduc...

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

Two solid circular shafts of $${{R_1}}$$ and $${{R_2}}$$ are subjected to same torque. The maximum shear stresses developed in the two shafts are $${\tau _1}$$ and $${\tau _2}.$$ I...

A cantilever beam of length, $$L,$$ with uniform cross-section and flexural rigidity $$ EI,$$ is loaded uniformly by a vertical load, $$w$$ per unit length. The maximum vertical de...

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

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...

Consider a simply supported beam of length $$50$$h, with a rectangular cross-section of depth h, and width $$2$$h. The beam carries a vertical point load P, at its mid-point. The r...

A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissible working stress is restricted to 100 MPa. The minimum cyl...

A simply supported beam of length $$L$$ is subjected to a varying distributed load $$\sin \left( {3\pi x/L} \right)N{m^{ - 1}},$$ where the distance $$x$$ is measured from the left...

A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress de...

For a ductile material, toughness is a measure of

Two threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt A is 4 times that of bolt B and the mean...

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 $$250$$ o C. If the Young's modu...

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'...

A cantilever beam of length $$L$$ is subjected to a moment $$M$$ at the free end. The moment of inertia of the beam cross section about the neutral axis is $$I$$ and the Young’s mo...

The state of stress at a point under plane stress condition is $${\sigma _{xx}} = 40\,$$ MPa, $${\sigma _{yy}} = 100\,$$ MPa & $${\tau _{xy}} = 40$$ MPa. The radius of the Mohr's c...

A solid circular shaft needs to be designed to transmit a torque of 50N.m. If the allowable shear stress of the material is $$140$$MPa, assuming a factor of safety of $$2,$$ the mi...

For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is

A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure rem...

A column has a rectangular cross-section of 10 mm $$ \times $$ 20 mm and a length of 1 m. The slenderness ratio of the column is close to

The state of plane-stress at a point is given by $${\sigma _x}\,\, = 200$$ MPa, $${\sigma _x}\,\, = 100$$ MPa and $${\tau _{xy}} = 100$$ MPa. The maximum shear stress (in MPa) is

A solid circular shaft of diameter $$d$$ is subjected to a combined bending moment, $$M$$ and torque, $$T.$$ The material property to be used for designing the shaft using the rela...

If the principal stresses in a plane stress problem are $${\sigma _1}$$ $$= 100$$ MPa, $${\sigma _2}$$ $$= 40$$ MPa, the magnitude of the maximum shear stress (in MPa) wil be

A compression spring is made of music wire of $$20$$ mm diameter having a shear strength and shear modulus of $$800$$ MPa and $$80$$ GPa respectively. The mean coil diameter is $$2...

A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 MPa. It further subjected to a torque of 10 KN-m. The maximum principal stress experienced on the sh...

A two dimensional fluid element rotates like a rigid body. At a point within the element, the pressure is $$1$$ unit. Radius of the Mohr's circle, characterizing the state at that...

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 l...

A pin-ended column of length $$L,$$ modulus of elasticity $$E$$ and second moment of the cross-sectional area $$I$$ is loaded centrally by a compressive load $$P.$$ The critical bu...

For a circular shaft of diameter $$'d'$$ subjected to torque $$T,$$ the maximum value of the shear stress is

A simply supported beam of span length $$6$$m and $$75$$ mm diameter carries a udl of $$1.5$$ kN/m What is the maximum value of bending stress?

A simply supported beam of span length $$6$$m and $$75$$ mm diameter carries a udl of $$1.5$$ kN/m What is the maximum value of bending moment?

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 th...

A weighing machine consists of a 2 kg pan resting on a spring in this condition, with the pan resting on the spring, the length of the spring is 200 mm. When a mass of 20 kg is pla...

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 longitud...

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

A solid circular shaft of $$60$$ mm diameter transmits a torque of $$1600$$ N - m. The value of maximum shear developed 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...

Maximum shear stress developed on the surface of a solid circular shaft under pure torsion is 240 MPa. If the shaft diameter is doubled then the maximum shear stress developed corr...

The state of stress at a point P in a two dimensional loading is such that the Mohr's circle is a point located at 175 MPa on the positive normal stress axis. The distance of maxim...

The beams, one having square cross section and another circular cross-section,are subjected to the same amount of bending moment. If the cross sectional area as well as the materia...

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 $$0.3$$...

A shaft subjected to torsion experiences a pure shear stress $$\tau $$ on the surface. The maximum principal stress on the surface which is at $$45$$ 0 to the axis will have a valu...