Home » Mechanical Engineering » Strength of Materials

Relation between shear force and bending moment: extremum condition For a loaded beam, use V = dM/dx. State the value/nature of bending moment at a point where the shear force is zero.

Difficulty: Easy

Zero
Minimum
Maximum
Infinite

Correct Answer: Maximum

Explanation:

Concept/Derivative relation
Shear force V = dM/dx. When V = 0, the slope of the bending-moment diagram is zero; therefore, M has an extremum (maximum or minimum) at that location.

Engineering usage
In most practical positive-moment regions of simply supported beams, the zero-shear point corresponds to the maximum bending moment.

Common pitfall
Remember it is an extremum in general. With usual loading on simply supported beams, that extremum is the maximum sagging moment.

Final Answer
Maximum.

← Previous Question Next Question→

More Questions from Strength of Materials

Dam engineering: identify the possible failure modes of a masonry dam Consider a gravity or masonry dam resting on soil or rock foundation. Assess the typical structural failure modes that may cause distress or collapse. Choose the correct comprehensive statement.
Strength of materials terminology: name the energy stored under elastic loading When a body is loaded within the elastic limit, it stores recoverable energy. Identify the correct term for this stored energy (overall, not per unit volume).
Axial stress in a tapering bar: where is the maximum stress located? A bar has a tapering cross-section along its length and carries a constant axial force. State the point along the bar where the axial normal stress is maximum. Choose the correct location.
Torsion formula terminology: identify J/R in the torsion equation Using the torsion relation T/J = τ/R = Gθ/L for circular shafts. State the standard name of the quantity J/R. Choose the correct term.
Bearing stress control in dams: limiting base stress against permissible soil stress For a masonry/gravity dam, to prevent crushing of masonry at the base, compare the maximum base stress with the soil’s permissible compressive stress. Choose the correct relation.
Strain measurement devices: purpose of a strain rosette (commonly misspelled as resetter) A strain rosette comprises multiple gauges at known angles bonded at a point on a surface. Identify what it directly measures. Choose the correct option.
Thermal stress in an unconstrained bar: heating a free steel bar from 15°C to 40°C A steel bar is heated from 15°C to 40°C and is perfectly free to expand (no constraint). State the stress induced in the bar as a result of heating. Choose the correct option.
Strain energy in a solid circular shaft under torsion: expression in terms of τ and C A solid circular shaft is subjected to torsion; let τ denote maximum shear stress and C the shear modulus (modulus of rigidity). Express the total strain energy stored in the shaft in the form (factor) × Volume of shaft. Choose the correct factor.
Basic definition in mechanics of materials: deformation per unit length In axial loading, the ratio of change in length to the original length is termed as what? Choose the correct term.
Column buckling: direction of failure based on principal second moments of area A vertical column has two principal moments of inertia Ixx and Iyy about orthogonal centroidal axes. Identify the direction in which the column will tend to buckle first under axial compression. Choose the correct option.

Discussion & Comments

No comments yet. Be the first to comment!

Join Discussion