Single-Bay Portal Frame with Unequal End Conditions A single-bay, single-storey portal frame has a hinged (pin) left support and a fixed right support. The beam carries a uniformly distributed load across the span. Considering frame action and stiffness asymmetry, indicate the direction of lateral sway under loading.

Introduction / Context:
Portal frames subjected to vertical loads may experience lateral sway when the end conditions or column stiffnesses are asymmetric. This sway arises because vertical loading induces unbalanced end moments and horizontal reactions that are not mirror-symmetric. Understanding the sway direction helps in assigning the correct sign for joint displacements and internal forces during analysis (slope-deflection, moment distribution, or stiffness method).

Given Data / Assumptions:

• Single-bay, single-storey portal frame.
• Left support: hinged (no moment resistance).
• Right support: fixed (full moment resistance).
• Beam loading: uniformly distributed load across span.
• Columns prismatic and of comparable stiffness (unless stated otherwise).

Concept / Approach:

Under UDL, the beam tends to sag, generating end moments at the column–beam joints. The fixed right support can resist moment and develops rotational restraint, while the hinged left support cannot. The imbalance of rotational restraints produces a net horizontal shear that drives the frame to translate laterally toward the more flexible side—the hinged support—resulting in leftward sway.

Step-by-Step Solution:

Verification / Alternative check:

Performing a first-order stiffness-method analysis with joint translations included shows a lateral DOF with nonzero displacement to the left. Classical examples in structural analysis texts report the same qualitative outcome.

Why Other Options Are Wrong:

• Rightward sway: would require opposite stiffness asymmetry or different loading eccentricity.
• No sway: would occur only for symmetric restraints and geometry under symmetric vertical loading.
• None of the above: unnecessary, as leftward sway is the recognized behavior here.

Common Pitfalls:

Assuming vertical loads never cause sway; neglecting joint translation DOFs; misinterpreting “fixed” versus “hinged” boundary conditions in moment distribution set-ups.

Final Answer:

It would sway to the left side