ENGG1400 Statics Prac S2 2020
Introduction
This guide describes how to set up and perform experimental tests to obtain the bending moments
and shear forces in beams. It clearly demonstrates the principals involved and gives practical
support to your studies on internal shear forces and bending moments in beams.
Part 1: Bending Moments in a Beam
In Part 1 of the
experiment,
we
shall
focus
our
attention in determining the bending moments in beams. Figure 1 shows the set up for this part
of the experiment. It consists of a beam, which is ‘cut’ by a pivot. In order to stop the beam from
collapsing, a moment arm bridges the cut onto a load cell; the measured force is then converted
to the bending moment by multiplying the force A diagram on the left-hand support of the beam
shows the beam geometry and hanger positions. Hanger supports are 20mm apart, and have a
centre slot, which positions the hangers. The moment arm is 125mm long.
with the lever arm. A digital display shows the force from the load cell.
Figure 1: Experimental set up for determining bending moment in beam
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ENGG1400 Statics Prac S2 2020
How to set up the equipment
The beam bending experiment fits into a test frame as shown in Figure 2.
Never apply excessive loads to any part of the equipment.
Figure 2: Beam bending experiment in a structural frame
Steps l to 4 of the following instructions have already have been completed for you.
1. Place assembled Test Frame (refer to the separate instructions supplied with the Test
Frame if necessary) on a workbench. Make sure the ‘window’ of the Test Frame is easily
accessible.
2. There are four securing nuts in the top member of the frame. Slide them to approximately
the positions shown in Figure 3.
3. With the right-hand and of the experiment resting on the bottom member of the Test
Frame, fit the left-hand support to the top member of the frame. Push the support on the
frame to squarely. Tighten the support in position by screwing two of the thumbscrews
provided into the securing nuts (on the front of the support only).
4. Lift the right-hand support into position and locate the two remaining thumbscrews into
the securing nuts. Push the support on to the frame to ensure the internal bars are sitting
on the frame squarely. Position the support horizontally to the rolling pivot is in the middle
of its travel. Tighten the thumbscrews.
5. Make sure the digital force display is ‘on’. 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.
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ENGG1400 Statics Prac S2 2020
6.
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.
Note: if the meter is only ±0.1N, lightly tap the frame (there may be a little suction and this should overcome it).
Experiments
Experiment 1: Bending Moment Variation at the Point of Loading
This experiment examines how bending moment varies at the point of loading. Figure 3 shows the free body diagram of
the beam with the load W and the reaction forces RA and RB. From statics consideration, RA= W(l-a)/l and RB=Wa/l.
300mm
440mm
Figure 3: Free body diagram of beam
The bending moment (BM) at the cut is given by
BM (at cut) = 𝑊𝑎
(𝑙 − 𝑎)
𝑙
You may find Table 1 useful in converting the masses used in the experiments to loads.
Table 1 Grams to Newtons conversion table
Mass (Grams)
Load (Newtons)
100
0.98
200
1.96
300
2.94
400
3.92
500
4.90
(a)
Check that the Digital Force Display meter reads zero with no load.
(b)
Place a hanger with a 100 gm mass at the ‘cut’. Record the digital force display reading in a table as in Table
1. Repeat using masses of 200 gm, 300 gm, 400 gm and 500 gm.
(c)
Convert the mass into a load (in N) and the force reading into a bending moment (Nm). Remember:
Bending moment at the cut (in Nm) = displayed force × 0.125
(d)
Calculate the theoretical bending moment at the cut and complete Table 2.
(e)
Calculate the percentage error
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ENGG1400 Statics Prac S2 2020
Table 2 Results for Experiment 1
Mass
(gm)
Load
(N)
Displayed
Force
(N)
Experimental
bending moment
(Nm)
Theoretical
bending moment
(Nm)
Percentage
difference
between
experimental
and
theoretical
bending
moments
0
0
0
0
0.000
0%
100
0.98
0.8
0.1
0.094
6.45%
200
1.96
1.6
0.2
0.187
6.45%
300
2.94
2.3
0.2875
0.281
2.39%
400
3.92
3.1
0.3875
0.374
3.44%
500
4.90
3.8
0.475
0.468
1.53%
What does it tell us about how bending moment varies at the point of loading?
The bending moment is directly proportional to the load applied (theoretically,
newton of applied in this case).
21
220
increase per
Does the equation we used accurately predict the behaviour of the beam?
The equation somewhat accurately predict the behaviours of beams (greatest deviation being of
6.45%).
Graph next page
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ENGG1400 Statics Prac S2 2020
Plot a graph which compares your experimental results to those you calculated by using the
theory. Comment on the shape of the graph.
Load vs Bending Moment
6
5
Load (N)
4
Experimental
3
Theoretical
2
Linear
(Experimental
)
Linear
(Theoretical)
1
0
0
0.1
0.2
0.3
0.4
0.5
Bending Moment (Nm)
Comment: The Load applied increases linearly with the bending moment. The trendline shows this
linearity.
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ENGG1400 Statics Prac S2 2020
Experiment 2：Bending Moment Variation away from the Point of Loading
This experiment examines how bending moment varies at the cut position of the beam for various
loading conditions. Figures 4, 5 and 6 show the free body diagrams for various loading positions
considered.
Figure 4: Free body diagram of beam with load at 140 mm to the left of support A
Figure 5: Free body diagram of beam with two loads W1 and W2 at 220mm and 260mm to the
right of support A
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ENGG1400 Statics Prac S2 2020
Figure 6: Free body diagram of beam with two loads W1 and W2 at 240mm and 400mm to the
right of support A
“The Bending Moment at the ‘cut’ is equal to the algebraic sum of the
moments caused by the forces acting to the left or right of the cut.”
(a) Check the Digital Force Display meter reads zero with no load.
(b) Carefully load the beam with the hangers in the positions shown in Figure 4, using the loads
indicated in Table 3. Record the Digital Force Display reading in a table as in Table 2.
(c) Convert the force reading into a bending moment (in Nm). Remember:
Bending moment at the cut (in Nm) = displayed force × 0.125
(d) Calculate the support reactions (𝑅𝐴 and 𝑅𝐵 ) and calculate the theoretical bending moment
at the cut.
(e) Repeat the procedure with the beam loaded as in Figure 5 and Figure 6.
(f) Comment on how the results of the experiments compare with those calculated using the
theory.
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ENGG1400 Statics Prac S2 2020
Table 3 Results for Experiment 2
-1.5
Experimental
bending
moment
(Nm)
-0.1875
3.92
3.7
3.92
4.0
𝑊1
𝑊2
(N)
(N)
Displayed
Force
(N)
4
3.92
0
5
1.96
6
4.91
Figure
𝑅𝐴
𝑅𝐵
(N)
(N)
5.167
-1.247
Theoretical
bending
moment
(Nm)
-0.175
0.4625
2.584
3.296
0.462
0.5
2.588
6.242
0.482
The experimental results closely resemble those found by the theory.
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ENGG1400 Statics Prac S2 2020
Part 2: Shear Forces in a Beam
In Part 2 of the experiment, we will look at determining the shear forces in beams. Figure 7 shows
the set up for this part of the experiment. 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
to a load cell thus activating (and measuring) the shear force. A digital display shows the force
from the load cell. A diagram on the left-hand support of the beam shows the beam geometry and
hanger positions. Hanger supports are 20 mm apart, and have a central groove which positions the
hangers. Figure 8 shows the experimental set up assembled in the Frame.
Figure 7: Experimental set up for determining shear forces in beam
.
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ENGG1400 Statics Prac S2 2020
Figure 8: Shear force of a beam experiment in the structures frame
Experiment 3: Shear force Variation at the Point of Loading
This experiment examines how the shear force varies at the point of loading. Figure 9 shows the
free body diagram for the beam with the applied load W.
260m
m
Figure 9: Free body diagram
The following equation will be used in this experiment
Shear force at cut, 𝑆𝑐 =
𝑊𝑎
𝑙
where 𝑎 is the distance to the load (not the cut), 𝑎 = 260 mm
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ENGG1400 Statics Prac S2 2020
(a) Check the digital force display meter reads zero with no load.
(b) Place a hanger with a 100 gm mass to the left of the ‘cut’ (40mm away). Record the Digital
Force Display reading in a table as in Table 2. Repeat using masses of 200 gm, 300 gm, 400
gm and 500 gm. Convert the mass into a load (in N)
Remember: Shear force at the cut = Displayed force
(c) Calculate the theoretical shear force at the cut and complete Table 4.
Table 4 Results for Experiment 3
Theoretical shear
force
(N)
Percentage
difference between
experimental and
theoretical shear
force
Mass
(gm)
Load
(N)
Experimental shear
force
(N)
0
0
0
0.000
0%
100
0.98
0.6
0.579
3.485%
200
1.96
1.1
1.158
5.289%
300
2.94
1.8
1.737
3.485%
400
3.92
2.3
2.316
0.711%
500
4.90
2.7
2.895
7.239%
What does it tell us about how shear force varies due to an increased load?
The shear force increases proportionally to the load applied (in this case
13
𝑊)
22
Does the equation we used accurately predict the behaviour of the beam?
Yes, although a little divergence at a greater load could be seen in the Plot. Greatest deviation is
5.389%.
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ENGG1400 Statics Prac S2 2020
Plot a graph which compares your experimental results to those you calculated using the
theory.
Comment on the shape of the graph.
Load vs Shear Force
6
5
Load (N)
4
Experimental
3
Theoretical
Linear
(Experimental)
2
Linear
(Theoretical)
1
0
0
0.5
1
1.5
2
2.5
3
3.5
Shear Force (N)
Comment: A linear trend between the Load and Shear Force can be seen. As the load was
increased, so did the shear force.
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ENGG1400 Statics Prac S2 2020
Experiment 4: 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. Figure 10, Figure 11 and Figure 12 show the positions of the various loading
positions considered.
Figure 10: Loading W1 on the beam at 140mm to the left of support A
Figure 11: Loadings W1 and W2 on the beam at 220mm and 260mm to the right of support A
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Figure 12: Loadings W1 and W2 on the beam at 240mm and 400mm to the right of support A
“The Shear force at the ‘cut’ is equal to the algebraic sum of
the forces acting to the left or right of the cut.”
(a) Check the Digital Force Display meter reads zero with no load.
(b) Carefully load the beam with the hangers in the positions shown in Figure 10, using the
loads indicated in Table 5. Record the Digital Force Display reading in a table as in Table
2.
(c) Record the Digital Force Display reading as in Table 3. Remember,
Shear force at the cut (N) = Displayed force
(d) Calculate the support reactions (𝑅𝐴 and 𝑅𝐵 ) and calculate the theoretical shear force at
the cut.
(e) Repeat the procedure with the beam loaded as in Figure 11 and Figure 12.
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ENGG1400 Statics Prac S2 2020
Table 5 Result for Experiment 4
Figure
𝑊1 (N)
𝑊2 (N)
Experimental shear
force (N)
𝑅𝐴 (N)
𝑅𝐵 (N)
Theoretical shear
force (N)
4
3.92
0.0
-1.3
5.167
-1.247
1.247
5
1.96
3.92
3.2
2.584
3.296
-3.296
6
4.91
3.92
2.3
2.588
6.242
-2.322
Comment on how the results of the experiments compare with those calculated using the
theory.
The results gave the opposite signs. The magnitudes were very similar. This could be due to a
different sign convention being used.
Theoretical calculations on following pages
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