Are you ready to test your preparation for the APPSC AEE 2026 Exam? Paper 2 (Strength of Materials) is known to be the toughest scoring section. To help our students practice, Mahesh IES Academy has compiled this exclusive 75 MCQ Model Paper directly from previous APPSC exams.
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Q.1) In which of the following the centroid lies outside the section?
a) Symmetrical I-section
b) Tee-section
c) Unsymmetrical I-section
d) Angle section
Q.2) It is preferable that the resultant transverse load on a beam may pass through the shear centre of the section, otherwise ______ will be induced on the beam
a) shear lag
b) torsion
c) unsymmetrical bending
d) crippling
Q.3) Shear flow on a section indicates:
a) shear stresses at the neutral axis
b) shear force per unit length
c) shear resistance of the section
d) shear force per unit depth
Q.4) 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 the cross-section of the beam is called
a) Moment centre
b) Centroid
c) Shear centre
d) Elastic centre
Q.5) The shear centre for an angle section is located ____.
a) at the rigidity centre of the angle
b) at the intersection of flanges
c) at the centroid of the angle
d) at the tip of the flange
Q.6) A beam has a circular cross section. If the plane of loading on the beam does not coincide with the centroidal axis of the beam the member is subjected to _____.
a) axial force, shear force and torque
b) torque, shear force
c) torque, shear force and bending moment
d) axial force, shear force and bending moment
Q.7) If the load does NOT passes through shear centre of the section of the beam, then there will be
a) No bending of the beam
b) Only bending of the beam
c) Only twisting of the beam
d) Both bending and twisting of the beam
Q.8) Shear centre is a point through which the load should act in a member such that
a) Only twisting acts and no bending
b) Bending and twisting act
c) Shear and bending acts but no twisting
d) Only shear acts and no bending and twisting
Q.9) The variation of shear along the line AB in the cross-section shown in figure (the member is used as a beam)
a) linearly varying from zero at A to maximum at B.
b) parabolically varying with maximum at C
c) triangularly varying with maximum at C
d) constant along AB
Q.10) The capacity of the beam to resist external transverse loads does not depend on
a) the cross-sectional properties of the material
b) the strength of the beam material
c) the span of the beam
d) elastic properties of the material
Q.11) The maximum shearing stress in beams of cross-sections having horizontal axis of symmetry occurs
a) at centre of gravity of the section
b) at about mid-depth of the section
c) at farthest point from the centre of gravity of the section
d) at a quarter depth from the top or bottom of the cross-section
Q.12) The ratio of maximum shear to the mean shear stress in case of a beam of circular cross section is
a) 4:3
b) 3:2
c) 5:4
d) 2:1
Q.13) The ratio of maximum shear stress developed in a beam of rectangular section that of the average shear stress is
a) 4/3
b) 3/4
c) 3/2
d) 2/3
Q.14) A beam of square cross-section with side 10mm is placed with one diagonal vertical. If the shear force acting on the section is 10 kN, the maximum shear stress is
a) 1 N/mm²
b) 1.125 N/mm²
c) 2 N/mm²
d) 2.25 N/mm²
Q.15) A beam of triangular cross-section is placed with its base horizontal. The maximum shear stress intensity in the section will be
a) at the neutral axis
b) at the base
c) above the neutral axis
d) below the neutral axis
Q.16) A beam of I section 600mm deep and 200mm wide has flanges 50mm thick and web 20mm thick. If the shear stress in the web is ‘τ’ then the shear stress in the flange at the junction is
a) τ
b) 0.1 τ
c) 10 τ
d) none
Q.17) The ratio of max. shear stress to average shear stress in a beam of circular cross-sections is
a) (1.0)
b) (1.33)
c) (1.5)
d) (1.88)
Q.18) In case of a beam for the same shear force, a rectangular section when compared with circular section of the same area of cross section is
a) stronger
b) weaker
c) equal
d) none of these
Q.19) In case of a beam of rectangular cross section the maximum shear stress developed is N times the average shear stress where
a) N = 1
b) N = 1.5
c) N = 2
d) N = 4
Q.20) The variation of shear stress over the cross section of a beam of T-section is
a) rectangular
b) parabolic
c) parabolic with a step
d) parabolic with two steps
Q.21) The ratio of the moment of inertia of a square plate to that of the circular plate of the same depth is
a) 1.563
b) 1.571
c) 1.698
d) 3.141
Q.22) The radius of gyration of a section is proportional to the square root of the
a) depth of the section
b) inverse of its area
c) inverse of its second moment of area
d) inverse of its first moment of area
Q.23) Along the neutral axis of a simply supported beam
a) fibre undergoes minimum strain
b) fibre does not undergo strain
c) fibre undergoes maximum strain
d) none of these
Q.24) A rectangular beam²0 cm wide is subjected to a maximum shearing force of 1000 kg, the corresponding maximum shearing stress being 5 kg/cm². The depth of the beam is
a) 15 cm
b) 20 cm
c) 25 cm
d) 30 cm
Q.25) The ratio of the moment capacity of a square section with its sides horizontal to that of the section with its diagonal horizontal is
a) 2.0
b) 0.577
c) 1.414
d) 0.707
Q.26) The moment of inertia of a beam of T section is 0.012 m 4 . The flange of the beam is 0.3 m wide and 0.1 m deep. The neutral axis of the beam is 0.25 m below the top of the flange. If the shear force on the section is 720 kN, the maximum shear stress in the flange is ___ N/mm²
a) 0.72
b) 0.6
c) 1.2
d) 2.4
Q.27) A beam of rectangular section 100 mm x 200 mm carries a shear force of 400 kN. The maximum shear stress in beam is
a) 30 MPa
b) 20 MPa
c) 33 MPa
d) 40 MPa
Q.28) For which of the following beam sections, will the shear stress be not maximum at the neutral axis? (assume the cross sectional area is same for all the cross-sections)
a) T section
b) Circular section
c) Triangular Section
d) Pipe Section
Q.29) Identify the shear free condition from among the following:
a) A bolt under tension
b) A concrete cube under compression
c) Surface of a spherical shell under internal pressure
d) A thick cylinder under fluid pressure
Q.30) A cantilever beam of T-section carries uniformly distributed load. The maximum shear stress occurs
a) at top of cross-section
b) at the junction of the web and flange
c) at neutral axis
d) at the bottom of the section
Q.31) For which of the following sections, will the shear centre lie outside the section?
a) Angle section
b) Tee section
c) Channel section
d) I section
Q.32) When a rectangular beam is loaded longitudinal shear develops on
a) top fibre
b) middle fibre
c) bottom fibre
d) every horizontal plane
Q.33) For a beam subjected to transverse shear force, the shear stress in the upper fibre will be
a) maximum
b) minimum
c) zero
d) depends on other data
Q.34) A circular section with area 100 mm² is subjected to a transverse shear force 6 kN. The magnitude of the maximum shear stress developed at the section is
a) 100 N/mm²
b) 80 N/mm²
c) 120 N/mm²
d) 40 N/mm²
Q.35) Flexural shear stresses do not have the maximum value at the neutral axis for a section of the profile:
a) rectangle
b) triangle
c) circle
d) square
Q.36) The fraction of S.F sustained by the web of rolled steel I section is about:
a) 0.35
b) 0.55
c) 0.75
d) 0.90
Q.37) The maximum shear stress developed in a beam of circular section is the average shear stress
a) equal to
b) 4/3 times
c) 1.75 times
d) 1.5 times
Q.38) In the case of H-section the maximum shear stress will occur at
a) top fibres
b) bottom fibres
c) neutral axis
d) the junction of the web and flanges
Q.39) When a rectangular beam is loaded transversely, the maximum tensile stress is developed on
a) the top layer
b) the bottom layer
c) the neutral axis
d) top layer in a cantilever
Q.40) At the neutral axis of a rectangular beam, the shear stress is
a) zero
b) minimum
c) maximum
d) infinity
Q.41) The maximum shear stress developed in a beam of rectangular cross-section is __ the average shear stress.
a) equal to
b) 4/3 times
c) 1.5 times
d) twice
Q.42) The bending stress at the neutral axis is
a) Zero
b) Maximum tensile
c) Minimum compressive
d) Minimum tensile
Q.43) In case of an I-section beam maximum shear stress is at
a) the junction of the top flange and web
b) middle of the web
c) top of the section
d) within the flange
Q.44) The shear stress distribution across a circular section is
a) circular
b) parabolic
c) hyperbolic
d) elliptic
Q.45) The shear stress on a rectangular beam section is max.
a) on the extreme free surface fibres
b) at the centroid of the section
c) at the NA
d) at the free edges
Q.46) The ratio of the max. shear stress to the average shear stress of a rectangular section or rectangular beam is
a) 2
b) 1.75
c) 1.5
d) None of the above
Q.47) In I section, almost all the shear force is taken by
a) Web
b) Top flange
c) Bottom flange
d) Both the flanges
Q.48) At the neutral axis of a beam cross-section
a) Bending stress is zero
b) Bending stress is maximum
c) Torsional stress is maximum
d) None of the above
Q.49) In a beam of circular cross-section, the average shear stress is 1.8 N/mm². The maximum shear across the section is
a) 2.7 N/mm²
b) 2.4 N/mm²
c) 2.2 N/mm²
d) 2 N/mm²
Q.50) A uniform I-section consists of 150 mm × 10 mm flanges and 10 mm x 100 mm web. The shear stress at the junction is 6 N/mm² for the flange portion. Then the shear stress at the same junction increases to _____ for the web portion.
a) 30N/mm²
b) 60N/mm²
c) 90N/mm²
d) 120N/mm²
Q.51) In a beam of rectangle cross-section of 150 mm x 300 mm, the maximum shear stress is ___for an applied shear force of 150 kN.
a) 5 N/mm²
b) 8 N/mm²
c) 12 N/mm²
d) 15 N/mm²
Q.52) In a rectangular block under a state of pure shear, the ratio of its diagonal longitudinal strain to the shear strain is
a) one
b) two
c) three
d) half
Q.53) The distribution of stress in a beam of rectangular cross-section is
a) Triangular
b) Parabolic
c) Rectangular
d) Elliptical
Q.54) The ratio of maximum to mean shear stresses across a circular cross-section is
a) 2.00
b) 1.50
c) 1.33
d) 1.25
Q.55) The cross-section of a beam is that of al triangle with a width of 0.4 m and a height of 0.6 m. If the section is subjected to a shear force of 6 kN, the maximum shear stress across the beam section is
a) 15kN/m²
b) 30kN/m²
c) 50kN/m²
d) 75kN/m²
Q.56) The ratio of maximum shear stress to the average shear stress in case of a rectangular beam is equal to
a) 1.5
b) 2.0
c) 2.5
d) 3
Q.57) The nature of distribution of horizontal shear stress in a rectangular beam is
a) linear
b) parabolic
c) hyperbolic
d) elliptic
Q.58) A beam of square section is placed with one diagonal placed horizontally. The maximum shear stress occurs at
a) the N.A.
b) d from top
c) d from N.A
d) at the extreme fibres Where d =depth of the beam
Q.59) In a beam of I section, the maximum shear force is carried by
a) the upper flange
b) the web
c) the lower flange
d) Any of these
Q.60) The ratio of maximum shear stress to average shear stress is 1.5 in a beam of
a) Circle
b) Rectangle
c) Triangle
d) Any cross-section
Q.61) A beam of square cross-section with side 100 mm is placed with one diagonal, vertical. If the shear force acting on the section is 10 kN, the maximum shear stress is
a) 1 N/mm²
b) 1.125 N/mm²
c) 2 N/mm²
d) 2.25 N/mm²
Q.62) In a case of a circular section, the maxi,um shear stress is ______ percent more than the mean shear stress.
a) 10
b) 20
c) 33.33
d) 66.66
Q.63) For a circular cross section subjected to shear force, the ratio of maximum shear stress to average shear stress is __ _.
a) 4/3
b) 2.0
c) 1.5
d) 1.0
Q.64) A rectangular section of a beam is acted upon by certain amounts of shear force and bending moment. Whereas the shear stress varies __ , the variation of bending stress is ___ along the depth.
a) linear with zero value at centroid, parabolic with zero value at top & bottom.
b) parabolic with zero value at centroid, linear with zero value at centroid.
c) parabolic, with zero value at top & bottom, linear with zero value at middle.
d) linear with zero value at centroid, linear with zero value at centroid.
Q.65) In case of an I-beam, major percentage of the shear force at a section is resisted by
a) Top flange
b) Bottom flange
c) Top and bottom flanges together
d) Web
Q.66) A rectangular beam²00 mm wide and 400 mm deep spans over a distance of 4 meters and carries a uniformly distributed load 40 kN/m. Determine the maximum shear stress acting on the beam cross section
a) 1.5 N/mm²
b) 1.0 N/mm²
c) 3.0 N/mm²
d) 2.0 N/mm²
Q.67) The ratio of the max. shear stress to the mean shear stress in case of a beam of triangular cross section is
a) 3:2
b) 2:3
c) 4:3
d) 3:4
Q.68) If the average shear stress in a rectangular section beam is 5 N/sq. mm, then maximum shear stress for the circular section of the equal area is
a) 6.65 N/sq. mm
b) 2.50 N/sq. mm
c) 10 N/sq.mm
d) 7.50 N/sq.mm
Q.69) In an I section, most of the shear force will be taken by
a) web
b) top flange
c) near to web
d) bottom flange
Q.70) For a solid circular section, the shear stress distribution is according to a
a) parabolic law
b) linear law
c) cubic law
d) constant
Q.71) The ratio of maximum to mean value of shear stress in a circular section is
a) 1.75
b) 1.5
c) 1.25
d) 1.33
Q.72) A simply supported beam of rectangular cross-section 100 mm x 200 mm carrying a concentrated load at mid-span. If the maximum shear stress developed in the beam is 3 MPa, what is the magnitude of concentrated load?
a) 20 kN
b) 40 kN
c) 80 kN
d) 160 kN
Q.73) A timber beam is simply supported at the ends and carries a concentrated load at mid span. The maximum longitudinal stress ‘f’ is 12 N/mm² and the maximum shear stress ‘q’ is 1.2 N/mm² . The ratio of span to depth would be
a) 10
b) 6
c) 5
d) 4
Q.74) For a beam of rectangular section under bending the shear stress across the depth varies
a) Linearly
b) Exponentially
c) Hyperbolically
d) Parabolically
Q.75) In the cross-section of rectangular beam, what is the ratio of the average shear stress to the maximum shear stress?
a) 3/2
b) 2/3
c) 4/3
d) 3/4
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