Description

Report writing: Use the template provided for writing your report
Submission Method: Online submission on TEAMS (submission box will be made available in week 08)

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 116 in Willis Annex (J18). Choose a partner within the group and attend the experiment as a pair. Each pair will work on one of the rigs for half an hour and on the other rig for further half an hour. Time is short, so come prepared to do measurements and leave your calculations until after you leave the laboratory. Videos explaining the experimental procedure are available on Moodle.
The report will be given a mark out of 6. The marking criteria are included at the end of this document.

How students will perform experiments and submit the report
To perform these four experiments in each part you are asked to work in a pair. You will have to select different variables required for the experiments. Before the selection process, described below, you should choose one of the pair and write his/her student number in Table 1 of the report template available on Moodle and use that student number for selecting proper load and distance from supports to perform all 8 experiments.
Students in the same pair should do all the experiments together and record values in the appropriate tables in the report template.

Figure 2: Digital Force Display Unit Figure 3: Load carrying hooks with masses

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.
Carefully zero the force meter using the dial on the left-hand support. 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.
1. EXPERIMENT 1: Shear force variation with an increasing point load
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 groups will perform the same experiment, using the same values for a, l, and W.

Figure 4: Experiment 1 set-up and Force Diagram

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

………….. (1)
where a 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.
Table 1: Grams to newtons Conversion Table
Mass (g) Load (N)
100 0.98
200 1.96
300 2.94
400 3.92
500 4.90

Check that the DFD meter reads zero with no load.
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:
𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑠ℎ𝑒𝑎𝑟 𝑓𝑜𝑟𝑐𝑒 𝑎𝑡 𝑡ℎ𝑒 𝑐𝑢𝑡 = 𝐷𝑖𝑠𝑝𝑙𝑎𝑦 𝑓𝑜𝑟𝑐𝑒 ……….….. (2)
2. EXPERIMENT 2: Shear Force variation away from the point of loading
This experiment examines how Shear Force varies at the cut position,C, for various loading conditions. W1 and a vary depending on the student number.

Figure 5: Experiment 2 set-up and Force Diagram
The Shear Force at the cut position, C, is equal to the algebraic sum of the forces acting to the left and the right of C.
Check the DFD meter reads zero with no load.
Carefully load the beam with the hanger in the position specified in Figure 5. Record the force reading on the meter in Table 3 of the template.
Calculate the support reactions RA and RB 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.
3. EXPERIMENT 3: Shear Force variation away from the point of loading
This experiment examines how Shear Force varies at the cut position, C, for various loading conditions.
Dimensions a and b and loads W1 and W2 vary depending on the student number.

Figure 6: Experiment 3 set-up and Force Diagram

The Shear Force at the cut position, C, is equal to the algebraic sum of the forces acting to the left and the right of C.
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 4 of the template.
Calculate the support reactions RA and RB 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
This experiment examines how Shear Force varies at the cut position, C, for various loading conditions.
Dimensions a and b and loads W1 and W2 vary depending on the student number.

Figure 7: Experiment 4 set-up and Force Diagram

The Shear Force at the cut position, C, is equal to the algebraic sum of the forces acting to the left and the right of C.
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 5 of the template.
Calculate the support reactions RA and RB 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.

This experiment examines how Bending Moment varies with increasing point load in a beam.
Instrumentation
Figure 8 shows the complete experimental frame with the DFD unit in position.

Figure 8: Bending Moment of a beam experimental frame
5. EXPERIMENT 1: Bending Moment variation at the point of loading
This experiment examines how Bending Moment varies at the point of loading. Figure 9 shows the equipment set-up and the force diagram for the beam. All groups will perform the same experiment, using the same values for a, l, and W.

Figure 9: Experiment 1 set-up and Force Diagram

The equation to be used to calculate the theoretical Bending Moment at the cut is:

………….. (3) Note: This equation is only for experiment 1 and should not be used for the rest of the experiments.
Check that the DFD meter reads zero with no load.
Place a hanger with a 100g mass at the cut. Record the force reading in Table 6 of the template. Repeat, using masses of 200g, 300g, 400g and 500g. Convert the mass into a load (in N) and the force reading into a Bending Moment (N·m). Remember, the experimental Bending Moment at the cut for all experiments is:
𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝐵. 𝑀 𝑎𝑡 𝑡ℎ𝑒 𝑐𝑢𝑡 (N. m) = 𝐷𝑖𝑠𝑝𝑙𝑎𝑦 𝑓𝑜𝑟𝑐𝑒 × 0.125 ……….. (4)

6. EXPERIMENT 2: Bending Moment variation away from the point of loading
This experiment examines how bending moment varies at the cut position, C, for various loading conditions. W1 and a vary depending on the student number.

Figure 10: Experiment 2 setup and force diagram

The Bending Moment at the cut position, C, is equal to the algebraic sum of the moments caused by the forces acting to the left and the right of C.
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 7 of the template.
Determine the value of RB for the calculation of the B.M. at C since it will be easier to evaluate the bending moment with the single value of RB than using W and RA to the left of C.
7. EXPERIMENT 3: Bending Moment variation away from the point of loading
This experiment examines how Bending Moment varies at the cut position, C, for various loading conditions. Dimensions a and b and loads W1 and W2 vary depending on the student number.

Figure 11: Experiment 3 setup and force diagram
The Bending Moment at the cut position, C, is equal to the algebraic sum of the moments caused by the forces acting to the left and the right of C.
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 8 of the template.
Convert the force readings into bending moments (N·m). First, calculate the support reactions RA and RB and then determine the B.M. at the cut, C.

8. EXPERIMENT 4: Bending Moment variation away from the point of loading
This experiment examines how Bending Moment varies at the cut position, 𝐶, for various loading conditions.
Dimensions 𝑎 and 𝑏 and loads W1 and W2 vary depending on the student number.

Figure 12: Experiment 4 setup and force diagram
The Bending Moment at the cut position, C, is equal to the algebraic sum of the moments caused by the forces acting to the left and the right of C.
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 9 of the template. Convert the force readings into Bending Moments (N·m). First, calculate the support reactions RA and RB and then determine the B.M. at the cut, C.

Figure 13: Distances from 𝑅𝐴

Appendix: Marking criteria for PART A: Shear-Force in a Beam
Criterion 0 marks 1 mark 2 marks 3 marks
SF expt 1. Theoretical values match calculation in marking spreadsheet Do not match All values match (should be correct to 1 decimal place) – –
SF expt 1 Plot of theoretical vs experimental results Incomplete / very messy plot Non-linear results for either set of data points or widely divergent results. Clear plot showing similar results, both theoretical and experimental results are linear. –
SF expt 1 discussion No attempt to justify error Basic restating of the facts evident in the plot. Mention of error but no discussion of error sources Errors discussed to an appropriate level in the space provided.
SF expt 2 calculations and
theoretical results with an FBD Clear error in calculation causing incorrect theoretical value Correct theoretical value but incorrect experimental value or vice versa with a wrong diagram A mistake in theoretical or experimental values with the correct diagram Both theoretical and
experimental values correct with the correct diagram
SF expt 3 calculations and
theoretical results with an FBD Clear error in calculation causing incorrect theoretical value Correct theoretical value but incorrect experimental value or vice versa with a wrong diagram A mistake in theoretical or experimental values with the correct diagram Both theoretical and
experimental values correct with the correct diagram
SF expt 4 calculations and
theoretical results with an FBD Clear error in calculation causing incorrect theoretical value Correct theoretical value but incorrect experimental value or vice versa with a wrong diagram A mistake in theoretical or experimental values with the correct diagram Both theoretical and
experimental values correct with the correct diagram
SF overall conclusion
(no need to draw a SFD) Invalid comments and No attempt to justify error Restating the conclusions without answering the question and Basic restating of the facts. Mostly correct comments without full understanding and Mention of error but no discussion of error sources Excellent correct discussion and Errors discussed to an appropriate level in the space provided.

Appendix: Marking criteria for PART B: Bending-Moment in a Beam
Criterion 0 marks 1 mark 2 marks 3 marks
BM expt 1 Theoretical values match calculation in marking spreadsheet with a correct diagram A wrong value and a wrong diagram All values match (should be correct to 1 decimal place), but a wrong diagram (Or vice versa) All values match (should be correct to 1 decimal place) with a correct diagram –
BM expt 1 Plot of theoretical vs experimental results Incomplete / very messy plot Non-linear results for either set of data points or widely divergent results. Clear plot showing similar results, both theoretical and experimental results are linear. –
BM expt 1 discussion No attempt to justify error Basic restating of the facts evident in the plot. Mention of error but no discussion of error sources Errors discussed to an appropriate level in the space provided.
BM expt 2 calculations and theoretical results with the correct diagram. Clear error in calculation causing incorrect theoretical value Correct theoretical value but incorrect experimental value or vice versa with a wrong diagram A mistake in theoretical or experimental values with the correct diagram Both theoretical and
experimental values correct with the correct diagram
BM expt 3 calculations and theoretical results with the correct diagram. Clear error in calculation causing incorrect theoretical value Correct theoretical value but incorrect experimental value or vice versa with a wrong diagram A mistake in theoretical or experimental values with the correct diagram Both theoretical and
experimental values correct with the correct diagram
BM expt 4 calculations and theoretical results with the correct diagram. Clear error in calculation causing incorrect theoretical value Correct theoretical value but incorrect experimental value or vice versa with a wrong diagram A mistake in theoretical or experimental values with the correct diagram Both theoretical and
experimental values correct with the correct diagram
BM overall conclusion Invalid comments and No attempt to justify error Restating the conclusions without answering the question and Basic restating of the facts. Mostly correct comments without full understanding and Mention of error but no discussion of error sources. Excellent correct discussion (in association with Part A) and Errors discussed to an appropriate level in the space provided.
Overall quality of report / formatting / plotting quality Basic, followed template with minimal modification Average formatting and comment. Professional quality of presentation, but the introduction is not at the highest level. Professional quality of presentation with a good introduction.