SOM: Assertion and Reasoning Type Questions

Assertion: If a rigid body is in equilibrium then the vector sum of the forces acting on the body is zero.

Reason: Vanishing of the resultant of the forces acting on a rigid body is a sufficient condition for the body to be in equilibrium.

Assertion: Strain is a fundamental behavior of the material, while stress is a derived concept.

Reason: Strain does not have a unit while stress has unit.

Assertion: Strain is a fundamental behavior of the material, while the stress is a derived concept.

Reason: Strain does not have a unit while the stress has a unit.

Assertion: The amount of elastic deformation at a certain point, which an elastic body undergoes, under given stress is the same irrespective of the stresses being tensile or compressive.

Reason: The modulus of elasticity and Poisson’s ratio are assumed to be the same in tension as well as compression.

Assertion: A mild steel tension specimen has a cup and cone fracture at failure.

Reason: Mild steel is weak in shear and failure of the specimen in shear takes place at 45° to the direction of the applied tensile force.

Assertion: In the case of a cylindrical structure carrying water under pressure, the maximum hoop stress is on a longitudinal plane through the centre of its cross-section.

Reason: The area of section of a cylinder by a longitudinal plane is inversely proportional to the chord length of the end section.

Assertion: The inclination of the line joining any point ‘p’ on the Mohr’s circle and the origin ‘o’ with x-axis equals twice the angle between the resultant stress and the normal of the plane for which P stands.

Reason: The inclination of the line joining any point ‘p’ on the Mohr’s circle and the centre of the circle ‘c’ with x-axis equals twice the angle between the planes for which P stands and zero degree plane.

Assertion: The maximum bending moment occurs where the shear force is either zero or changes sign.

Reason: If the shear force diagram line between the two points is horizontal, the BM diagram line is inclined. But if the SF (Shear Force) diagram is inclined, the BM diagram is a parabola of second degree.

Assertion: I-section is preferred to rectangular section for resisting bending moment.

Reason: In I-section more than 80% of bending moment is resisted by flanges only.

Assertion: A beam of circular cross-section in comparison to rectangular section of the same material but of equal cross-sectional area can resist a large shear force.

Reason: The maximum intensities of shear stress in the sections of a beam of circular cross-section are   1 1/3 times and 1 ½ times the average shear stress respectively.

Assertion: The buckling load for a column of specified material, cross-section and end conditions calculated as per Euler’s formula varies inversely with the column length.

Reason:  Euler’s formula takes into account the end conditions in determining the effective length of column.

Assertion: The Bending Moment (BM) due to any load at all sections of an arch, is less than the BM at all sections of a simple beam having the same span of arch under the same load.

Reason:  The moment due to horizontal thrust of the arch is hogging.

Assertion: In the analysis of rigid frames, the usual practice is to consider the strain energy due to flexure only.

Reason: The strain energies due to axial and shear forces are usually quite  small compared to that flexure.

Assertion: Whether it is maximum BM at a section or absolute maximum BM, the moving UDL should cover the entire span of a simple beam if span is less than load length.

Reason: Whether it is maximum BM at a section or absolute maximum BM, the moving UDL should be divided by the section in the same ratio in which the section divides the span is less than load length.