Lateral buckling of a discretely braced I-beam — parameter sensitivity For a symmetrical I-section beam with discrete lateral supports (i.e., the compression flange is laterally braced at intervals), the maximum allowable compressive stress corresponding to lateral–torsional buckling depends on several section and bracing properties. Which one of the following does it NOT depend upon?

Introduction / Context:
Lateral–torsional buckling (LTB) limits the compressive stress that can be safely developed in the compression flange of a beam between points of lateral restraint. For beams with discrete lateral bracing, the controlling length is the laterally unbraced segment, not the total span. This question asks which listed quantity does not influence the LTB allowable stress for such a beam.

Given Data / Assumptions:

• Symmetrical I-section beam.
• Discrete lateral supports along the span create an effective unbraced length L_b between braces.
• Elastic LTB formulation applies (serviceability/allowable stress perspective).

Concept / Approach:
In classic elastic LTB, the critical stress (or moment) depends on modulus of elasticity E, torsional/warping properties (J, Cw), weak-axis bending stiffness (I_y → radius of gyration r_y), and the effective unbraced length L_b. Section plate proportions like overall depth to flange thickness affect J, Cw, and thus the LTB resistance. The global span length however does not directly enter the LTB formula when intermediate bracing defines L_b; only the unbraced segment length matters.

Step-by-Step Solution:
Identify the controlling length: L_b (distance between lateral restraints), not the full span.Recognize dependencies: E and r_y appear in the critical stress expression; flange/web proportions influence J and Cw.Note that changing overall span without changing brace spacing leaves L_b unchanged → no change in allowable LTB stress.Therefore, the parameter that does not govern the LTB allowable stress is the overall span length.

Verification / Alternative check:
Design equations express M_cr ∝ E * function(J, Cw, I_y) / L_b, or equivalent stress forms with L_b. Nowhere does the full span appear unless L_b equals the span (no intermediate bracing).

Why Other Options Are Wrong:
Modulus of elasticity (a) directly influences stiffness and buckling resistance. Radius of gyration about the minor axis (b) affects lateral rigidity. Depth/thickness ratio (d) alters torsional/warping properties, thus influencing LTB.

Common Pitfalls:
Confusing total span with unbraced length; overlooking the role of warping stiffness; assuming material yield strength, rather than E, controls elastic LTB.

Final Answer:
the span length of the beam