Steel Design – Critical Compression Stress in Bending (Sections Symmetrical about x–x Axis) In the standard formula for the critical compression stress Cs used for lateral–torsional behaviour, the shear modulus G is conventionally taken as a proportion of the Young’s modulus E for structural steel. What value of G is generally adopted for design calculations?

Introduction / Context:In steel design, the critical compression stress in bending for members susceptible to lateral–torsional buckling depends on elastic constants. Two key constants are the Young's modulus E and the shear modulus G. Designers often need a reliable value of G, expressed as a fraction of E, to evaluate buckling resistance for sections symmetrical about the x–x axis.

Given Data / Assumptions:

• Material: structural steel with Poisson's ratio approximately 0.3.
• Relationship between elastic constants: G = E / (2 * (1 + nu)).
• Design practice uses rounded proportions of E for G.

Concept / Approach:

The shear modulus G links shear strain to shear stress and appears in lateral–torsional buckling expressions. Using nu around 0.3, one can estimate G as a consistent fraction of E for routine design without detailed material testing.

Step-by-Step Solution:

Verification / Alternative check:

If nu varies slightly (for example 0.28 to 0.31), G changes only marginally, remaining very close to 0.38 E to 0.39 E. Thus 0.4 E is a safe, conventional approximation.

Why Other Options Are Wrong:

• 0.2 E: Far below the physical value implied by nu ≈ 0.3, overly conservative and incorrect.
• 0.3 E: Still too low relative to E / 2.6 ≈ 0.385 E.
• 0.5 E: Much higher than realistic shear modulus for steel, unconservative.

Common Pitfalls:

Confusing G with E, or assuming G equals E / 3 by rule of thumb without checking nu. Always use the relation G = E / (2 * (1 + nu)).

Final Answer:

0.4 E