Rectangular steel column base plate (slab base) thickness for uniform bearing Let w be the uniform bearing pressure on concrete (force per unit area) and m be the projection of the base plate beyond the column face. Determine the plate thickness t for a cantilever projection behaving as a plate strip.

Introduction:In steel design, a slab base (base plate) spreads column load to concrete. The plate projects beyond the column face and behaves like a cantilevered strip under uniform bearing pressure. Correct thickness ensures bending stresses remain within the permissible value.

Given Data / Assumptions:

• w = uniform bearing pressure on concrete under the plate.
• m = projection of plate beyond the column face measured to the edge.
• sigma_b = permissible bending stress in the plate steel.
• Strip theory: plate projection behaves as a cantilever of unit width.

Concept / Approach:

For a cantilever strip of unit width loaded by uniform pressure w over length m, the resultant load is w * m and the bending moment at the fixed edge is M = w * m^2 / 2 per unit width. The section modulus of a plate strip of unit width is Z = t^2 / 6.

Step-by-Step Solution:

Verification / Alternative check:

Design thickness should also satisfy local checks near anchor bolts and consider biaxial projections if m differs on two sides; adopt the larger required t.

Why Other Options Are Wrong:

Options A and B underestimate thickness (unconservative). Option D overestimates bending effect excessively. Option E is dimensionally inconsistent for plate thickness.

Common Pitfalls:

Using gross plate width instead of projection m; neglecting grout stiffness; ignoring the weaker projection side when projections differ.

Final Answer:

t = m * sqrt( 3 * w / sigma_b )