SUPPORT REACTION OF A SIMPLY SUPPORTED BEAM AND A
CONTINUOUS BEAM
AIM
The purpose of this lab is to validate the basic beam equilibrium RA + RB = w
and the principle of moments for finding the reactive beams and to investigate
the reactions of a two-span continuous beam with three supports.
INTRODUCTION
A beam is said to be in equilibrium when there is no tendency for it to move. It
is vital in analyzing the supportive reactions [1]. A simply supported beam is
one that rests on two supportive polls and is free to move horizontally.
Ordinary viable uses of simply supported beams with point loadings
incorporate extensions, beams in structures, and beds of machine devices. A
continuous is an underlying part that provides resistance to bending when a
load or force is applied [2]. In contrast to a simply supported beam, which
upholds at each end and a heap is disseminated somehow or another along its
length, a continuous beam is a lot stiffer and more grounded. A continuous
beam has a large number of supports than are needed to give balance, and the
disfigurement conduct under load is additionally viewed as while deciding the
help responses. The end spans might be cantilever, might be openly supported
of fixed supported.
Method- Experiment 1
1. Open the application (VDAS) and select “STS13 Continuous and
Indeterminate Beams” experiment.
2. Select “Simply Supported Beam – Point Loads” experiment.
3. The default parameters correspond to the experiment nomenclature
where the Length of the beam is 850mm. The applied mass to the beam
would be 500g. The experiment does not require I or E.
4. Switch tabs from “Data Acquisition” to the “Simulation tab”. The
experiment requires only W1, so W2 and W3 had zero masses.
5. Results are taken from the “Results” section of VDAS.
6. Used the Principle of static equilibrium and moments from “Results” to
calculate theoretical values of RA and RB.
Method- Experiment 2
1. Open VDAS and select “Continuous and Indeterminate Beams”
experiment.
2. Select “Continuous Beam” experiment.
3. Put in Values for W1 and W2.
4. The Results are taken from the “Results” section of VDAS.
5. Record the beam reactions RA, RB and RC.
6. Calculate the theoretical values of RA, RB and RC.
Results and Analysis
Experiment 1
Table 1: Simulation Results for Experiment One
Distance(l1-x)
(mm)
50
100
150
200
250
300
350
400
450
Load W
(N)
4.9
4.9
4.9
4.9
4.9
4.9
4.9
4.9
4.9
RA
(N)
4.42
3.93
3.44
2.94
2.45
1.96
1.47
0.98
0.49
RB
(N)
0.49
0.98
1.47
1.96
2.45
2.94
3.44
3.93
4.42
RA+RB
(N)
4.91
4.91
4.91
4.91
4.91
4.91
4.91
4.91
4.91
Table 2: Theoretical Values for Experiment 1
Distance A
(mm)
50
100
150
200
250
300
350
400
450
Load W
(N)
4.9
4.9
4.9
4.9
4.9
4.9
4.9
4.9
4.9
RA
(N)
4.61
4.32
4.04
3.75
3.46
3.17
2.88
2.59
2.31
RB
(N)
0.29
0.58
0.86
1.15
1.44
1.73
2.02
2.31
2.59
RA+RB
(N)
4.9
4.9
4.9
4.9
4.9
4.9
4.9
4.9
4.9
Calculation for RA and RB:
𝑅𝐵 =
=
𝑊×𝐴
𝐿
(4.9)(0.050)
0.85
𝑅𝐵 = 0.288235294 𝑁
𝑅𝐴 = 𝑊 − 𝑅𝐵
= 4.9 − 0.288235294
𝑅𝐴 = 4.61176 𝑁
5
4,5
RA and RB (N)
4
3,5
3
2,5
RA
2
RB
1,5
1
0,5
0
50
100
150
200
250
300
350
400
450
Distance(mm)
Figure 1: Shows the relationship of RA and RB against distance
Experiment 2
Table 1: Simulation Results for Experiment 2
Config LC (m)
1
0.075
2
0.125
3
0.155
LE(m)
0.075
0.088
0.075
W1(N) W2(N)
4.91
4.91
5.89
8.83
6.87
4.91
RA(N)
1.08
1.82
1.55
RB(N)
6.67
10.07
9.08
RC(N) M(N.m)
2.06
0.11
2.83
0.28
1.55
0.27
Table 2: Theoretical Calculations for Experiment 2
Config
1
2
3
LA
(m)
LB
(m)
LC
(m)
LD
(m)
LE
(m)
LF
(m)
W1 W2 RA
(N) (N) (N)
RB
(N)
RC
M
(N) (N.m)
0.125 0.125 0.075 0.050 0.075 0.050 4.91 4.91 1.08 6.67 2.06
0.250 0.175 0.125 0.125 0.088 0.087 5.89 8.83 1.83 10.07 2.83
0.5 0.375 0.250 0.250 0.188 0.187 7.85 3.92 2.85 8.39 0.53
Calculation for M, RA, RB and RC:
M=
RA=
RB=
RC=
(𝑊1×𝐿𝐶×𝐿𝐷)×(𝐿𝐴+𝐿𝐶)
1
(
2(𝐿𝐴+𝐿𝑏)
𝑊1.𝐿𝐶−𝑀
𝐿𝐴
(𝑊2×𝐿𝐸×𝐿𝐹)×(𝐿𝐵+𝐿𝐹)
𝐿𝐵
) = 0.110363 𝑁. 𝑚
= 1.0791 𝑁
𝑊1×𝐿𝐶+𝑀
𝐿𝐴
𝑊2×𝐿𝐸−𝑀
𝐿𝐵
𝐿𝐴
+
+
𝑊2×𝐿𝐷+𝑀
𝐿𝐵
= 6.6708 𝑁
= 2.0601 𝑁
Discussion and Questions
Experiment 1
Questions
1. Figure 1 shows a straight-line graph of the two reactive forces where it
shows RA and RB are directly proportional to distance.
2. After conducting a simulation in VDAS, the theoretical values do not
match the simulation. The theoretical values must have gone wrong in
the calculation area.
3. The potential sources of error would be human errors as everyone is
not perfect.
4. Support reactions values were not predicted by the static equilibrium as
static equilibrium was not equal to zero but more or less than zero
Discussion
The results for table 1 was determined by the use of VDAS. For the
theoretical RA values, it was found using the formula given. As the distance
increase, the RA values starts to decease. And for the RB values, as the
0.11
0.28
0.54
distance increase RB also increases. And the total sum of the reactive forces
equals to the load. Theoretical values do not match the simulation as for
that an error must have occurred during the calculation. The graph shows
the relationship of the two reactive forces and it is directly proportional to
the distance.
Experiment 2
Questions
1. The theoretical values match the simulated values.
2. If the center support were to sink, reactions RA and RB would also go
down.
3. The type of ground that would be suitable to build footings on are a
fully compact ground where the ground would not crack under
pressure. This is not always possible because there are number of
waters stored under the ground and if it gets punctured water would
start to sip out and make the ground muddy.
Discussion
Experiment 2 was conducted by the use of VDAS. To get the values of M, RA,
RB and RC the length and mass was altered to run the simulation for different
values. After the simulation was completed the values of M, RA, RB and RC was
given. After the simulation, the next step is to calculate the theoretical values
using the same mass and lengths from the simulation. The values matched the
simulation therefore calculations conducted were successful.
Conclusion
To conclude the following experiment, the basic beam equilibrium equation
was used to find RA, RB and W. And also, the investigation for the reactions of
a two-mass beam with three supports found its values.
References
[1] C. M. C. J O Bird BSc, "Science Direct," Elsevier Ltd, 27 June 2014. [Online]. Available:
https://www.sciencedirect.com/science/article/pii/B9780750616836500394. [Accessed 3
September 2021].
[2] D. Distefano, "Info Bloom," 11 December 2013. [Online]. Available:
https://www.infobloom.com/what-is-a-continuous-beam.htm. [Accessed 3 September 2021].