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ENGG1300 Engineering Mechanics

Shear force and Bending Moment Lab

Overview

There are two parts in this lab – Part A: Shear-Force and Part B: Bending-Moment. Each part is carried out on a separate rig in the Undergraduate Teaching Laboratory (UTL) i.e. Room 214A in Willis Annex (J18). Each student will work on one of the Sheer-Force rigs for half an hour and on the Bending-Moment rig for another half hour. Time is short, so come prepared to do measurements and leave your calculations until after you leave the laboratory.

You can obtain access to the undergraduate teaching laboratory, room 214A of the Willis Annex building (J18), within your booked time-slot.

Before you enter the laboratory you need to have viewed the videos. You must gain competency in a Safe Work Procedure and Risk Management Form for the rigs prior to using the experimental equipment. Enclosed footwear is required to enter the laboratory. Follow the COVID safety guidelines during the whole experiment.

The marking criteria of the report are included at the end of this document. The mark will be then scaled to match the weight of the assignment on the overall mark for the course. 

How students will perform experiments and submit the report 

Five students are grouped to work together in each team. Each student will have different experimental data. To perform all experiments in each part, you will have to use your own zID for selecting proper load and distance (see Table in the next page). All students should submit different reports individually. All reports should be developed independently and no joint work is allowed except for the execution of the experiments in the lab.

Complete the report template (to be provided on Teams) and submit the report (one per student) as a PDF by the due date/time (see course outline and Teams announcements) for assessment. Note that unless all the workings areshown, full marks will not be awarded. You must type your report (including equations) and label all figures. Freehand FBDs and BMDs are accepted, but must be clean and neat.

Load selection variables based on student number

The typical student number has 7 digits. Label these from the left as a,b,c,d,e,f & g (e.g. for the student number 3295406 ‘a’ would equal 3 and ‘g’ would equal 6). Loads and distances that should be selected by each student are given in the table below.

Figure 1 shows the complete experimental frame with the Digital Force Display (DFD) unit in position. It consists of a beam which is “cut”. To stop the beam collapsing, a mechanism (which allows movement in the shear direction only) bridges the cut on a load cell thus reacting and measuring the Shear Force. DFD shows the force from the load cell.

PART A: SHEAR FORCE IN A BEAM - INTRODUCTION Make sure that the DFD is “ON”. Connect the mini DN lead from “Force Input 1” on the DFD to the socket marked “Force Output” on the left-hand support of the equipment. Ensure that the lead does not touch the beam.

This experiment examines how Shear Force varies with increasing point load. Figure 4 shows the equipment set-up and the force diagram for the beam. All students will perform the same experiment, using the same values for !, #, and (.

The equation to be used to determine the theoretical Shear Force at the cut is:

where ! is the distance from the load, not the cut, to the left support. Note: This equation is only for experiment 1 and should not be used for the rest of the experiments.

You may find the following table useful in converting the masses used in the experiments to loads.

Place a hanger with a 100g mass to the left of the cut (40mm away). Record the force reading on the meter in Table 2 of the template. Repeat using masses of 200g, 300g, 400g and 500g. Convert the mass into a load (in N). Remember, the experimental Shear Force at the cut in Newtons for all experiments is: :;<+,.=+>-!# 0ℎ+!, 12,/+ !- -ℎ+ /3- = ?.0<#!@ 12,/+ ……….….. (2)

2. EXPERIMENT 2: Shear Force variation away from the point of loading

This experiment examines how Shear Force varies at the cut position,4, for various loading conditions.(% and ! vary depending on the student number.

Figure 5: Experiment 2 set-up and Force Diagram

The Shear Force at the cut position, 4, is equal to the algebraic sum of the forces acting to the left and the right of 4.

3. EXPERIMENT 3: Shear Force variation away from the point of loading

The Shear Force at the cut position, 4, is equal to the algebraic sum of the forces acting to the left and the right of 4.

Check the DFD meter reads zero with no load.

Carefully load the beam with the hanger in the position specified in Figure 6. Record the force reading on the meter in Table 3 of the template.

Calculate the support reactions A& and A' and calculate the theoretical Shear Force at the cut.

Note: Depending on the sign convention chosen, the experimental and theoretical Shear Forces could have opposite signs. Therefore, you must specify your sign convention.

4. EXPERIMENT 4: Shear Force variation away from the point of loading

Check the DFD meter reads zero with no load.

Carefully load the beam with the hanger in the position specified in Figure 7. Record the force reading on the meter in Table 3 of the template.

Note: Depending on the sign convention chosen, the experimental and theoretical Shear Forces could have opposite signs. Therefore, you must specify your sign convention.This experiment examines how Bending Moment varies with increasing point load in a beam.

5. EXPERIMENT 1: Bending Moment variation at the point of loading

6. EXPERIMENT 2: Bending Moment variation away from the point of loading

This experiment examines how bending moment varies at the cut position, 4, for various loading conditions. W% and a vary depending on the student number.

The Bending Moment at the cut position, 4, is equal to the algebraic sum of the moments caused by the forces acting to the left and the right of 4.

Check the DFD meter reads zero with no load.

Carefully load the beam with the hanger in the position specified in Figure 10. Record the force reading on the meter in Table 5 of the template.

Determine the value of A' for the calculation of the B.M. at 4 since it will be easier to evaluate the bending moment with the single value of A' than using ( and A& to the left of 4.

7. EXPERIMENT 3: Bending Moment variation away from the point of loading

Figure 11: Experiment 3 setup and force diagram

The Bending Moment at the cut position, 4, is equal to the algebraic sum of the moments caused by the forces acting to the left and the right of 4.

Check that the DFD meter reads zero with no load.

Carefully load the beam with the hangers in the positions shown in Figure 11. Record the force reading on the meter in Table 5 of the template.

Convert the force readings into bending moments (N·m). First, calculate the support reactions A& and A' and then determine the B.M. at the cut, 4.

8. EXPERIMENT 4: Bending Moment variation away from the point of loading

This experiment examines how Bending Moment varies at the cut position, 4, for various loading conditions.

Dimensions ! and B and loads !! and !" vary depending on the student number.

Figure 12: Experiment 4 setup and force diagram

The Bending Moment at the cut position, 4, is equal to the algebraic sum of the moments caused by the forces acting to the left and the right of 4.

Check that the DFD meter reads zero with no load.

Carefully load the beam with the hangers in the positions shown in Figure 12. Record the force reading on the meter in Table 5 of the template. Convert the force readings into Bending Moments (N·m). First, calculate the support reactions A& and A' and then determine the B.M. at the cut, 4.140 mm