Structural Analysis & Design Flashcards

The flexure formula for bending stress in a beam is σ = Mc/I. What does 'c' represent?

Answer: The distance from the neutral axis to the outermost fiber

In σ = Mc/I, c is the perpendicular distance from the neutral axis to the extreme fiber where stress is maximum.

For a rectangular cross-section of width b and height h, the moment of inertia about the centroidal horizontal axis is:

Answer: bh³/12

The moment of inertia of a rectangle about its centroidal x-axis is I = bh³/12.

The maximum shear stress in a solid circular shaft of radius r subjected to torque T is given by:

Answer: τ = 2T/(πr³)

For a solid circular shaft, τ_max = Tr/J = T·r/(πr⁴/2) = 2T/(πr³).

Which theorem states that the deflection at point A due to a unit load at point B equals the deflection at B due to a unit load at A?

Answer: Maxwell's Reciprocal Theorem

Maxwell's Reciprocal Theorem states that flexibility coefficients are symmetric: δ_AB = δ_BA.

A beam has a shear force V, first moment of area Q, moment of inertia I, and width b at a cross-section. The horizontal shear stress is:

Answer: τ = VQ/Ib

The shear formula τ = VQ/(Ib) gives the average horizontal shear stress at a given level in a beam.

In Mohr's circle for plane stress, the center of the circle is located at:

Answer: ((σx + σy)/2, 0)

The center of Mohr's circle lies on the σ-axis at the average normal stress (σx + σy)/2, with zero shear.

Principal stresses are defined as the normal stresses that occur on planes where the shear stress is:

Answer: Zero

Principal planes are oriented so that shear stress vanishes, leaving only maximum and minimum normal stresses.