Lab 1

Winter 2013 Page 1 of 6

University of Ontario Institute of Technology Faculty of Engineering and Applied Science

ENGR 2420U Solid Mechanics

Laboratory Manual

LAB 1: SHEAR FORCE EXPERIMENT


Lab Objectives

In this module, you will set up and perform Shear Force in a Beam Experiments. It clearly demonstrates the principles involved and gives practical support to your studies. There are two experiments for this lab. Experiment 1 measures the shear force variation with an increasing point load. Experiment 2 measures the shear force variation for various loading conditions. Background Figure 1 shows the shear force of a beam experiment in the structures frame. Loads are applied to experiments using hangers which hold various masses. The digital Force Display electronically measures and displays forces during experiments. It is conveniently fixed to the Test Frame. At the end of this lab, you should be able to prove the following statement: “The Shear force at the ‘cut’ is equal to the algebraic sum of the forces acting to the left or right of the cut”.

Figure 1: Shear Force experiment

Equipment Figure 2 shows the Shear Force in a Beam experiment. It consists of a beam which is ‘cut’. To stop the beam from collapsing, a mechanism (which allows movement in the shear direction only) bridges the cut on to a load cell thus reacting (and measuring) the shear force. A digital display shows the force from the load cell. The masses supplied with the equipment give maximum flexibility and ease of use. Figure 3 shows a hanger loaded with masses. Use the clips provided to hold the masses on the hangers. There are one-hundred-and-fifty 10-gram masses and five 10-gram weight hangers. This allows any load, in increments of 10-grams, to be made up to a maximum 500-grams. Alternatively, one hanger can be made up into 100-grams, 200-grmas, 300-grams, 400-grams or 500-grams.


Figure 2: Shear force in a beam experiment

Figure 3: Hanger with masses

Safety Instructions There is a risk of electric shock. Always unplug first. During test do not touch any parts of the test apparatus except the designated

handles. IMPORTANT! Never attempt any form of machine maintenance. IMPORTANT! Never attempt to apply any excessive load over than the designed

loads; it may cause damage to the load cell and also plastic deformation in the beam.


Test Procedure

1. Turn ON the Digital Force Display. Connect the mini DIN lead from ‘Force Input 1’ on the Digital Force display to the socket marked ‘Force Output’ on the left-hand support of the experiment. Ensure the lead does not touch the beam.

2. Carefully ZERO the force meter using the dial on the left-hand beam of the experiment. Gently apply a small load with a finger to the centre of the beam and release. Zero the meter again if necessary. Repeat to ensure the meter returns to zero.

NOTES: If the meter is only +/-0.1N, lightly tap the frame (there may be a little ‘stiction’ and this should overcome it). IMPORTANT: NEVER apply excessive loads to any part of the equipment. Shear Force Variation with an Increasing Point Load

This experiment examines how shear force varies with an increasing point load. Figure 4 showsthe force free-body diagram for the beam.

Figure 4: Force free-body diagram

We can find the shear force at the cut section by following formula:

l

aFRV Bc

.

Check the Digital Force Display meter reads zero with no load. Place a hanger with a 100g mass to the left of the ‘cut’. Record the Digital Force Display reading in a table as in Table 1. Repeat using masses of 200g, 300g, 400g and 500g.


Remember, Shear force at the cut = Displayed force. Calculate the theoretical shear force at thecut and complete the table. Plot a graph which compares your experimental results to those you calculated using the theory. Comment on the shape of the graph. What does it tell us about how shear force varies due to and increased load? Does the equation we used accurately predict the behavior of the beam? Shear Force Variation for Various Loading Conditions

This experiment examines how shear force varies at the cut position of the beam for various loading conditions. Figures 5, 6 and 7 show the loading conditions and corresponding force iagrams. Check the Digital Force Display meter reads zero with no load. Carefully load the beam with the hangers in the positions shown in Figure 5, using the loads indicated in Table 2. Record the Digital Force Display reading in Table 2. Remember, Shear force at the cut (N) = Displayed force. Calculate the support reactions (RA and RB) and calculate the theoretical shear force at the cut. Repeat the procedure with the beam loaded as in Figure 6 and Figure 7. Plot a graph which compares your experimental results to those you calculated using the theory. Comment on how the results of the experiments compare with those calculated using the theory.


Lab Report A full report would usually require a brief outline of the steps taken in performing the experiment and of precautions taken to minimize errors. Your report should contain the following items:

1. A record of all measurements made on the test specimens 2. Tabulate needed values of Tables 1 and 2 for each load case 3. Plots showing variation of the load vs. shear force for both experiments

References: This document is adopted from a similar lab manual written by Dr.C. S. Tufekci

of UOIT and edited. Shear Force in a Beam: Lecturer Guide, TQ Education and Training Ltd. 1999-

2001 Shear Force in a Beam: Student Guide, TecQuipment Ltd. 1999. Hibbeler, R. C. Mechanics of Materials, 6/e, Prentice Hall, Upper Saddle River,

NJ, 2004.

Documents

Lab 1