Mechanics of Materials Flashcards

In the flexure formula σ = My/I, what does the variable 'y' represent?

Answer: The distance from the neutral axis to the point of interest

In the bending stress formula, y is the perpendicular distance from the neutral axis to the fiber where stress is being calculated.

For a simply supported beam of span L carrying a central point load W, the maximum bending moment is:

Answer: WL/4

Each reaction is W/2; the maximum moment at midspan = (W/2)(L/2) = WL/4.

The section modulus Z of a solid rectangular section (width b, height h) is:

Answer: bh²/6

Z = I / y_max = (bh³/12) / (h/2) = bh²/6; it directly gives maximum bending stress as σ = M/Z.

For a rectangular beam cross-section, where does the maximum shear stress due to transverse loading occur?

Answer: At the neutral axis

Shear stress is zero at the free (extreme) surfaces and reaches its maximum at the neutral axis for a rectangular section.

The second moment of area (moment of inertia) of a solid circular cross-section with diameter D about a centroidal axis is:

Answer: πD⁴/64

I = πD⁴/64 for a solid circle about a diameter; the polar moment of inertia J = 2I = πD⁴/32.

For a simply supported beam carrying a uniformly distributed load w (per unit length) over its full span L, the maximum bending moment is:

Answer: wL²/8

Maximum bending moment at midspan = wL²/8 for a UDL on a simply supported beam; the reactions are each wL/2.

The neutral axis of a beam cross-section under pure bending is the locus of points where:

Answer: Bending (normal) stress is zero

The neutral axis experiences neither tension nor compression during bending; normal stress is zero there and transitions from tensile to compressive across it.