Experiment No. 5:

Bending Moment In A Simply Supported Beam
Civil Engineering Laboratory II
CE407
Dr. Chris L. Mullen
University of Mississippi
Department of Civil Engineering

1.0 INTRODUCTION

1.1 The HST.1/11 setup for the Hi-Plan 2 Structures Apparatus is to used to determine the bending moment in a simply supported beam under a variety of loading patterns.

1.2 The objective is to observe the mechanism by which an internal action such as a moment may be measured and to compare the measured predictions with theoretical estimates obtained by elementary structural analysis such as influence lines.

2.0 THEORY

2.1 Definitions.

• Simply supported beam- horizontal member of length, L0, loaded transverse to its axis and supported at the ends in a manner which permits free rotations at the ends. All reactions and internal forces are statically determinate.
• Bending moment- internal force, M, acting at a cross section of the beam that maintains rotational equilibrium.
• Influence line- plot of response, e.g. bending moment at point x0, due to a unit load placed at variable positions, x, on the beam.

2.2 Analysis

1. Compute influence line, M(x) for a single load, F0=1, for given x0, L0, using equations of statics and elementary structural analysis. (See Structures Handout No. 1)
2. Use unit load analysis and the principle of superposition to estimate the moment at x0 for a variety of multi-load situations characteristic of highway vehicle loadings, given the relative position and intensity of the loads.

Alternatively, construct the bending moment diagram directly for the multi-load situations.

3.0 EQUIPMENT

The HST.1/11 setup is shown in the figure below. The spring balance is located underneath the two beam segments that are connected by a hinge and provides the only variable readout in the experiment.

4.0 EXPERIMENTAL PROCEDURE

Consider three load cases and compare the theoretical and experimental values.

Use measured values of lengths in all instances.

Note that in order to measure an internal response quantity, it is necessary to either implant something or to cut the member. Since the spring balance crosses the point of discontinuity in the beam it is able to develop the resisting moment. How?

• Load Case 1. A single 10 N weight is placed at the point of discontinuity. Measure the position from the left support.
• Load Case 2. One 5 N weight is placed at a position x0= .2 L0.
• Load Case 3. A single 10 N weight is placed at the point of discontinuity. Measure the position from the left support.

5.0 RESULTS AND CALCULATIONS

5.1 Data Collection/Results Table (Forms to be given in lab.)

Complete forms to be handed out in lab which summarize the recorded data , calculated predictions, and percent difference (error).

6.0 DISCUSSION

Comment on sources of error and random variation in recorded data.
Comment on possible explanation of differences between recorded data and theoretical predictions.

7.0 CONCLUSIONS

State what you accomplished through the experiment. Were your measurements reasonable? Was the apparatus well suited for this measurement? Do you have any suggestions to improve the procedure?