In a grillage footing supporting a steel column, where does the maximum shear force occur in the grillage system under axial load transfer?

Introduction / Context:
Grillage footings distribute heavy column loads to soil over a large plan area using tiers of steel beams. Understanding where maximum shear occurs in the grillage beams ensures proper web sizing and stiffener detailing.

Given Data / Assumptions:

• Axially loaded column with a base plate supported by orthogonal grillage beams.
• Load spreads from the base plate into the upper-tier beams as a concentrated line load near the plate edge.
• Symmetric arrangement and uniform soil reaction.

Concept / Approach:
The base plate acts like a load distributor. For each grillage beam, the critical section for shear is typically at the face of the concentrated load application, i.e., at or just outside the edge of the base plate (the face of the column projection onto the beam). Shear then reduces toward the beam ends as reactions distribute to the concrete.

Step-by-Step Solution:

Verification / Alternative check:
Run a simple beam idealization: a concentrated load near the beam centre has peak shear at the adjacent section; this aligns with standard detailing practices where stiffeners are placed near the base-plate edges.

Why Other Options Are Wrong:
Midspan shear is smaller; at the beam outer edge the shear has already diminished; uniform shear does not match statics of beam-and-soil reaction.

Common Pitfalls:
Ignoring the two-way action between orthogonal beams; omitting bearing stiffeners near the plate edge; assuming uniform soil reaction without checking differential settlement.

Final Answer:
At the edge of the base plate (face of the column projection)