For a tension member plate of width b and thickness t with staggered rivet holes, what is the correct expression for the net sectional area A_net in terms of staggered pitch p, gauge distance g, number of holes n, number of gauge spaces m, and rivet diameter d?

Introduction / Context:In riveted tension members, gross area is reduced by rivet holes. For staggered pitch, some strength is regained due to the zig-zag path. IS:800 specifies an effective net area formula considering both direct hole deduction and staggered layout benefit.

Given Data / Assumptions:

• b = plate width
• t = plate thickness
• n = number of rivet holes in zig-zag line
• m = number of gauge spaces in zig-zag line
• d = gross diameter of rivet hole
• p = staggered pitch
• g = gauge distance

Concept / Approach:Gross area = b*t. Hole deductions = n*d*t. Staggered arrangement adds a term (p^2 / (4g)) * m * t to account for the zig-zag path.

Step-by-Step Solution:Start with gross area: A_g = b*tDeduct holes: n*d*tAdd stagger correction: (p^2 / (4g)) * m * tNet area: A_net = b*t − n*d*t + (p^2 / (4g)) * m * t

Verification / Alternative check:Matches IS:800 and standard design handbooks for staggered connections.

Why Other Options Are Wrong:

• b*t − n*d*t: ignores staggered benefit
• b*t − (n−1)*d*t: incorrect deduction
• Negative stagger term: physically impossible

Common Pitfalls:Using clear hole diameter instead of gross; forgetting to add stagger term; mixing up m (spaces) vs n (holes).

Final Answer:A_net = b*t − n*d*t + (p^2 / (4g))*m*t