Weld / Combined Stresses – Equivalent (resultant) stress for combined bending tension and shear Given bending tensile stress fbt and shear stress fs at a point, choose the correct equivalent stress fe used for design checks.

Introduction / Context:
Connections and welds often experience simultaneous normal stress (from axial force or bending) and shear stress (from transverse loads or torsion). Design practice uses an equivalent stress to ensure the combined state does not exceed the allowable for the material and detail. This question probes the commonly used expression for combining bending tension and shear, especially for fillet weld throats and similar details.

Given Data / Assumptions:

• Normal (tensile) stress due to bending at the checked point = fbt.
• Shear stress at the same point = fs.
• Design per traditional Indian steel practice (working stress/allowable stress format) for weld/connection checks.

Concept / Approach:

A conservative and widely used interaction is based on the maximum shear (or distortion energy) theory adapted for weld design, leading to an equivalent resultant stress of the form fe = sqrt(fbt^2 + 3 * fs^2). The factor 3 reflects the relative contribution of shear in the combined state at the weld throat metal compared with pure normal stress.

Step-by-Step Solution:

Verification / Alternative check:

Where code permits the principal stress approach, results are similar in magnitude for typical ratios of fbt to fs. The chosen interaction has long-standing acceptance in weld design tables and examples.

Why Other Options Are Wrong:

sqrt(fbt^2 + fs^2) underestimates the influence of shear; linear addition fbt + fs lacks physical basis; the principal stress expression (fbt/2 + sqrt((fbt/2)^2 + fs^2)) gives a principal stress, not the weld-throat equivalent used in allowable-stress weld design.

Common Pitfalls:

Mixing limit-state factors with allowable-stress values, or evaluating stresses at mismatched locations (e.g., extreme fibre vs weld throat centreline).

Final Answer:

fe = sqrt(fbt^2 + 3 * fs^2)