Understanding Portal Frame Deformation Under UDL

This question concerns the deformation behavior of a specific type of structural frame, known as a portal frame, when subjected to a load.

Portal Frame Configuration:

• Type: Single bay, single storey portal frame. This consists of two vertical columns and one horizontal beam connecting their tops.
• Supports: The left support is hinged, meaning it allows rotation but prevents horizontal or vertical movement. The right support is fixed, preventing both rotation and movement.
• Loading: A uniformly distributed load (UDL) is applied to the beam, denoted as a load of w per unit length (w/m).
• Assumption: All members (columns and beam) have the same length.

Analysis of Deformation:

When a uniformly distributed load (UDL) is applied to the beam of a portal frame, the beam bends downwards, causing a sagging effect.

This downward deflection of the beam induces internal forces (bending moments and shear forces) in the columns at the points where they connect to the beam (the eaves).

These forces cause the columns to bend inwards, towards the center of the frame.

Influence of Support Conditions:

The way the frame deforms, specifically whether it sways (moves laterally), is significantly influenced by the type of supports:

• Hinged Left Support: This support allows the base of the left column to rotate freely. It offers less resistance to lateral movement compared to a fixed support.
• Fixed Right Support: This support rigidly holds the base of the right column, preventing both rotation and lateral movement. It offers high resistance to deformation.

Predicting Sway Direction:

The inward bending of the columns, caused by the beam's sag, results in a lateral displacement of the frame's top (the eaves level). This lateral movement is called sway.

Due to the asymmetric support conditions, the frame does not deform symmetrically. The structure tends to deform or sway towards the side that offers less resistance to movement.

In this case, the hinged support on the left provides less restraint than the fixed support on the right. Therefore, the inward bending effect caused by the UDL leads to a net lateral movement, or sway, towards the side with the hinged support.

Conclusion:

Given the hinged support is on the left and the fixed support is on the right, the portal frame will sway towards the left side under the effect of the uniformly distributed load on the beam.