Curved Bar Deflection

Name: Muhammad Faeq Ahmed

CMS: 503552

Section: C

Course: ME-115 Mechanics of Materials Lab

Institute: School of Mechanical & Manufacturing Engineering, NUST

Session: Spring 2026

Objective

The purpose of this experiment was to observe the deflection of a curved bar subjected to a concentrated vertical load and to compare the measured vertical and horizontal displacements with theoretical predictions. The test also aimed to confirm that the material remained within the linear elastic range as the applied load was increased step by step.

A curved bar does not behave exactly like a straight beam, so its deflection is commonly evaluated using an energy method. In this experiment, Castigliano’s theorem is used to estimate displacement from strain energy stored in bending. For small loads, the response should remain proportional to the applied force, which means the load–deflection graph is expected to be approximately linear.

The stiffness of the bar depends strongly on its cross-sectional dimensions. In particular, increasing the thickness raises the second moment of area, which reduces deflection significantly.

The specimen was a mild steel curved bar with a rectangular cross-section.

The experimental values show a nearly proportional increase with load, which supports the assumption of elastic behavior.

The data indicate a clear linear relationship between the applied load and the resulting deflections. This behavior suggests that the curved bar remained within its elastic limit throughout the test. The measured vertical displacements were slightly higher than the theoretical values, and the horizontal readings also showed small deviations.

The differences between theory and experiment may be caused by support flexibility at the clamped end, minor inaccuracies in specimen dimensions, dial gauge reading errors, vibration during measurement, and the effect of the hanger load not being fully included in the theoretical model. Despite these sources of error, the agreement between measured and predicted values was reasonably good.

This experiment confirmed that a curved bar under a small concentrated load responds in a linear elastic manner. The comparison between the observed and calculated deflections showed acceptable agreement, which supports the use of Castigliano’s theorem for curved members. The results also reinforced the fact that geometric properties, especially thickness and moment of inertia, have a major effect on stiffness and deflection.