GATE Civil Engineering

The three-dimensional state of stress at a point is given by $$\sigma = \begin{pmatrix} 10 & 0 & 0 \\ 0 & 40 & 0 \\ 0 & 0 & 0 \end{pmatrix} \text{ MPa.}$$ The maximum shear stress...

A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio (l/r) of 105, where l is the bar length and r is the radius of gyration. The coe...

A circular solid shaft of span L = 5 m is fixed at one end and free at the other end. A torque T = 100 kN.m is applied at the free end. The shear modulus and polar moment of inerti...

When a simply-supported elastic beam of span L and flexural rigidity EI (E is the modulus of elasticity and I is the moment of inertia of the section) is loaded with a uniformly di...

A 5 cm long metal rod AB was initially at a uniform temperature of T 0 °C. Thereafter, temperature at both the ends are maintained at 0°C. Neglecting the heat transfer from the lat...

A 2D thin plate with modulus of elasticity, 𝐸 = 1.0 N/m 2 , and Poisson’s ratio, 𝜇 = 0.5, is in plane stress condition. The displacement field in the plate is given by 𝑢 = 𝐶𝑥...

The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be 30.0 MPa. The value of maximum shear stress at this point is

For a linear elastic and isotropic material, the correct relationship among Young's modulus of elasticity (E), Poisson's ratio (v), and shear modulus (G) is

An elastic bar of length L, uniform cross sectional area A, coefficient of thermal expansion a, and Young’s modulus E is fixed at the two ends. The temperature of the bar is increa...

Consider two axially loaded columns, namely. $$1$$ and $$2,$$ made of a linear elastic material with Young's modulus $$2 \times {10^5}\,\,MPa,$$ square cross-section with side $$10...

A simply supported beam is subjected to a uniformly distributed load. Which one of the following statements is true?

A hollow circular shaft has an outer diameter of $$100$$ $$mm$$ and inner diameter of $$50mm.$$ If the allowable shear stress is $$125$$ $$MPa$$, the maximum torque (in $$kN$$-$$m$...

A simply supported reinforced concrete beam of length $$10$$ $$m$$ sags while undergoing shrinkage. Assuming a uniform curvature of $$0.004\,\,{m^{ - 1}}$$ along the span, the maxi...

In a system, two connected rigid bars $$AC$$ and $$BC$$ are of identical length $$L$$ with pin supports at $$A$$ and $$B.$$ The bars are interconnected at $$C$$ by a frictionless h...

The first moment of area about the axis of bending for a beam cross-section is

Polar moment of inertia $$\left( {{{\rm I}_p}} \right),$$ in $$c{m^4},$$ of a rectangular section having width, $$b=2$$ $$cm$$ and depth $$d=6$$ $$cm$$ is __________

A symmetric $${\rm I}$$-section (with width of each flange $$=50mm$$, thickness of each flange $$=10mm,$$ depth of web $$=100mm,$$ and thickness of web $$=10mm$$) of steel is subje...

Two steel columns $$P$$ (Length $$L$$ and yield strength $${f_y} = 250\,\,MPa)$$ and $$Q$$ (length $$2L$$ and yield strength $${f_y} = 500\,\,MPa$$) have the same cross-sections an...

The state of $$2D$$-stress at a point is given by the following matrix of stresses: $$$\left[ {\matrix{ {{\sigma _{xx}}} & {{\sigma _{xy}}} \cr {{\sigma _{xy}}} & {{\sigma _{yy}}}...

The ‘'plane section remains plane’' assumption in bending theory implies:

The following statements are related to bending of beams: $${\rm I}.$$ The slope of the bending moment diagram is equal to the shear force. $${\rm II}.$$ The slope of the shear for...

The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material, but with pinned ends, is equal to

A simply supported beam is subjected to a uniformly distributed load of intensity $$w$$ per unit length. On half of the span from one end. The length of the span and the flexural s...

If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cube is $$p,$$ then the maximum shear stress developed inside...

The Poisson's ratio is defined as

The major and minor principal stresses at a point are $$3MPa$$ and $$-3MPa$$ respectively. The maximum shear stress at the point is

The number of independent elastic constants for a linear elastic isotropic and homogeneous material is

The effective length of a column of length $$L$$ fixed against rotation and translation at one end is

Two people weighing W each are sitting on a plank of length $$L$$ floating on water at $$L/4$$ from either end. Neglecting the weight of the plank, the bending moment at the center...

A solid circular shaft of diameter d and length $$L$$ is fixed at one end and free at the other end. A torque t is applied at the free end. The shear modulus of the material is $$G...

Consider the following statements: $$1.$$ On a principal plane, only normal stress acts $$2.$$ On a principal plane, both normal and shear stresses act $$3.$$ On a principal plane,...

The point within the cross sectional plane of a beam through which the resultant of the external loading on the beam has to pass through to ensure pure bending without twisting of...

A hollow circular shaft has an outer diameter of $$100$$ $$mm$$ and a wall thickness of $$25$$ $$mm.$$ The allowable shear stress in the shaft is $$125$$ $$MPa.$$ The maximum torqu...

A vertical rod $$PQ$$ of length $$L$$ is fixed at its top end $$P$$ and has a flange fixed to the bottom end $$Q.A$$ weight $$W$$ is dropped vertically from a height $$h\left( { <...

A mild steel specimen is under uniaxial tensile stress. Young's modulus and yield stress for mild steel are $$2 \times {10^5}\,\,MPa$$ and $$250$$ $$MPa$$ respectively. The maximum...

A thin walled cylindrical pressure vessel having a radius of $$0.5$$ $$m$$ and wall thickness of $$25$$ $$mm$$ is subjected to an internal pressure of $$700$$ $$kPa$$. The hoop str...

The maximum shear stress in a solid shaft of circular cross-section having diameter subjected to a torque $$T$$ is $$\tau $$ . If the torque is increased by four times and the diam...

For an isotropic material, the relationship between the young’s modulus (E), shear modulus (G) and Poisson’s ratio (μ) is given by

A metal bar of length 100mm is inserted between two rigid supports and its temperature is increased by $$10^o$$C. If the coefficient of thermal expansion is 12 x$$10^{-6}$$ per $$^...

A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$\omega $$ per unit length. The beam has constant flexural rigidity...

The maximum and minimum shear stresses in a hollow circular shaft of outer diameter $$20$$ $$mm$$ and thickness $$2$$ $$mm,$$ subjected to a torque of $$92.7$$ $$N.m$$ will be

A steel column, pinned at both ends, has a buckling load of $$200$$ $$kN.$$ If the column is restrained against lateral movement at its mid-height, its buckling load will be

A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$\omega $$ per unit length. The beam has constant flexural rigidity...

The shear stress at the neutral axis in a beam of triangular section with a base of $$40$$ $$mm$$ and height $$20$$ $$mm,$$ subjected to a shear force of $$3$$ $$kN$$ is

An axially loaded bar is subjected to a normal stress of $$173$$ $$MPa.$$ The maximum shear stress in the bar is

A thin-walled long cylindrical tank of inside radius $$'r'$$ is subjected simultaneously to internal gas pressure $$P$$ and axial compressive force $$F$$ at its ends. In order to p...

A long shaft of diameter $$d$$ is subjected to twisting moment $$T$$ at its ends. The maximum normal stress acting at its cross-section is equal to

Mohr's cicle for the state of stress defined by $$\left[ {\matrix{ {30} & 0 \cr 0 & {30} \cr } } \right]$$ $$MPa$$ is a circle with

If a beam of rectangular cross-section is subjected to a vertical shear force $$V,$$ the shear force carried by the upper one-third of the cross-section is

The components of strain tensor at a point in the plane strain case can be obtained by measuring longitudinal strain in following directions.

The symmetry of stress tensor at a point in the body under equilibrium is obtained from

A circular solid shaft of span $$L=5m$$ is fixed at one end and free at the other end. A twisting moment $$T=100$$ $$kN$$-$$m$$ is applied at the free end. The torsional rigidity $...

If principle stresses in two-dimensional case are $$\left( - \right)\,\,10\,MPa$$ and $$20$$ $$MPa$$ respectively, then maximum shear stress at the point is

$${U_1}$$ and $${U_2}$$ are the strain energies stored in a prismatic bar due to axial tensile forces $${P_1}$$ and $${P_2},$$ respectively. The strain energy $$U$$ stored in the s...

A homogeneous, simply supported prismatic beam of width $$B,$$ depth $$D$$ and span $$L$$ is subjected to a concentrated load of magnitude $$P.$$ The load can be placed anywhere al...

For linear elastic systems, the type of displacement function for the strain energy is

A long structural column (length $$-L$$) with both ends hinged is acted upon by an axial compressive load $$P.$$ The differential equation governing the bending of column is given...

The shear modulus (G), modulus of elasticity (E) and the Poisson's ratio ($$\mu$$) of a material are related as

Pick the incorrect statement from the following four statements:

In a section, shear center is a point through which, if the resultant load passes, the section will not be subjected to any

A small element at the critical section of component is in a state of stress with the two principal stresses being $$360$$ $$MPa$$ and $$140$$ $$MPa$$ . The maximum shear stress is

A cantilever beam of span $$'L'$$ is loaded with a concentrated load $$'P'$$ at the free end. Deflection of the beam at the free end is

A propped cantilever beam of span $$L,$$ is loaded with uniformly distributed load of intensity $$w/unit$$ length, all through the span. Bending moment at the fixed end is

When a column is fixed at both ends corresponding to Euler's criterion load is

A beam fixed at the ends and subjected to lateral loads only is statically indeterminate and the degree of indeterminacy is

The fixed end moment of a uniform beam of span $$l$$ fixed at the ends, subjected to a central point load $$P$$ is

For a given shear force across a symmetrical $${\rm I}$$-section, the intensity of shear is maximum at

A cantilever beam of span $$l$$ subjected to a uniformly distributed load $$'w'$$ per unit length resting on a rigid prop at the tip of cantilever. The magnitude of the reaction of...

A cantilever beam curved in plan and subjected to lateral loads will develop at any section

The state of two dimensional stresses acting on a concrete lamina consists of a direct tensile stress, $${\sigma _x} = 1.5\,\,N/m{m^2},$$ and shear stress, $$\tau = 1.20\,N/m{m^2},...

Which of the following Mohr's circles shown below qualitatively and correctly represents the state of plane stress at a point in a beam above the neutral axis, where it is subjecte...

A cantilever beam of span, $$'L'$$ is subjected to a downward load of $$800$$ $$kN$$ uniformly distributed over its length and a concentrated upward load $$P$$ at its free end. For...

The axial load carrying capacity of a long column of given material. Cross-sectional area, $$A$$ and length, $$L$$ is governed by

The kern area (core) of a solid circular section column of diameter, $$D$$ is a concentric circle of diameter, $$'d'$$ is equal to

The maximum bending stress induced in a steel wire of modulus of elasticity $$200$$ $$kN/m{m^2}$$ and diameter $$1$$ $$mm$$ when wound on a drum of diameter $$1$$ $$m$$ is approxim...

In a real beam, at an end, the boundary condition of zero slope and zero vertical displacement exists. In the corresponding conjugate beam, the boundary conditions at this end will...

The moments at the end $$'A'$$ and $$'B'$$ of a beam $$'AB'$$ where end $$(a)$$ is fixed and $$(b)$$ is hinged, when the end $$(b)$$ sinks by an amount $$\Delta $$ are given as

The maximum value of Poisson's ratio for an elastic material is

A cantilever beam of tubular section consists of 2 materials copper as outer cylinder and steel as inner cylinder. It is subjected to a temperature rise of $$20^\circ C$$ and $$\al...

In a linear elastic structural element