In strength of materials notation, the transverse shear stress at a point in a beam cross-section is given by which general formula (use standard symbols: V = shear force at the section, Q = first moment of area about the neutral axis for the portion above/below the level of interest, I = second moment of area of the whole section about the neutral axis, b = local width at the level of interest)?

Introduction / Context:
Determining the distribution of shear stress across a beam's cross-section is essential for safe design. The standard formula uses the internal shear force and geometric properties of the section to evaluate transverse (vertical) shear at any fiber.

Given Data / Assumptions:

• Prismatic beam subjected to transverse loading that creates shear force V.
• Linear elastic behavior; small deformations.
• Symbols: V, Q, I, and b have their usual strength of materials meanings.

Concept / Approach:
The transverse shear stress is derived from equilibrium of an infinitesimal slice of the beam considering variation of bending stress along the depth. This leads to a relationship that links shear flow to the gradient of bending stress, which in turn depends on section geometry.

Step-by-Step Solution:

Verification / Alternative check:
For a rectangular section, insert Q and b to obtain the classic parabolic distribution with maximum f_s = 1.5 * V / A at the neutral axis, confirming the formula's correctness.

Why Other Options Are Wrong:
Options using M * y / I describe bending stress, not shear. Forms like V / (A * b) or (E * I) / (V * Q) do not follow from equilibrium or material laws and are dimensionally inconsistent for shear stress.

Common Pitfalls:
Using gross width instead of local width b at the level of interest; computing Q about the wrong axis; forgetting that Q is for the area above or below the point where stress is evaluated.

Final Answer:
f_s = (V * Q) / (I * b)