Abstract

This report presents the relationship between load and shear force under different conditions
and a comparison of experimental measured and theoretical values of shear force. The
experiment consists of two parts. The first part of the experiment was based upon the
variation in shear force by increasing point loads. The second part includes how shear force
varies under different load conditions at the cut position. The observation based on
calculation and plot showed that there was a direct relationship between shear force and
applied load because the value of shear force increased by increasing applied load. The
second part of the experiment proved that the shear force at the cut position is equal to the
sum of forces acting to the left or right of the cut. The experimental measured and
theoretically measured values are slightly different this might be due to error account during
the recording of the reading or inaccurate calibration of the instrument. Overall, the objective
of the experiment was achieved successfully.

Aims and Objective

This experiment aimed to measure the relationship between shear force and applied load
under different conditions and comparison of the experimental value of shear force with
theoretical results.

Introduction and Background

In construction, the beams are designed to manage the applied load. The common of road
bridges which mainly based upon beams, which are used to manage the point load, string of
wheel load, and uniformly distributed load or all three loads at a time [1]. When load acts on
the beam the applied forces or stress causes the beam to bead or produce elastic
deformation. The types of effect are generated in the beam mainly due to the vertical
component of forces that acts perpendicularly on the longitudinal axis of the beam. These
components of forces produce a shear force which is the relative movement of two parts of
the structure. The beams are designed in such a way to bear or resist against this shear
force [2]. Here this Lab demonstrates the process to calculate the acting shear force on the
beam due to applied load. The first part of this lab was used to examine the variation in
shear force by increasing point load. The second part demonstrates the shear force at a cut
point under different load conditions. In addition, the second part includes the verification of
the argument that the shear force at the cut position is equal to the algebraic sum of applied
forces from left or right to that cut point.

Methods
The digital force scale was set at zero and the mass of 100gm was attached to the cut
position. The experimental value of shear force was read from a digital scale and recorded in
Table. Similarly, the experiment was repeated for the mass of 200gm, 300gm, 400gm, and
400gm, and the experimental value of shear force was recorded in Table one. The
theoretical value of shear force is calculated from the following equation 1. The comparison
of the two values is shown in Graph shear force vs applied Load.
W .a
Theoretical shear force Value= (N) (1)
l
Where (w) is applied load, (a) is distance, and (l) is total span.
In the second experiment, the load was hung according to the given condition and
corresponding shear force values were measured from the force digital scale.
Results

 The obtained result from experiment 1 is listed in Table 1 for the Experimental and
Theoretical values for Shear force
 The plot between applied load and shear force (N) in the case of experimental and
theoretical values is shown in Figure 1.
 The obtained results from experiment 2 are listed in Table 2 for both experimental
and theoretical values of shear force
 The shear force graph for the condition given in figure 5 is shown in figure 2.
 The calculations are included in the appendix.

Table 1: Shear force(N) vs Applied Load (w)

Mass (gm) Load (N) Experimental Theoretical Error %
shear force Shear Force
(N) (N)
0 0 0 0 0
100 0.98 0.5 0.579 13.644
200 1.96 1.2 1.158 3.627
300 2.94 1.9 1.737 9.384
400 3.92 2.4 2.316 3.627
500 4.91 2.8 2.901 3.482

Shear Force vs load W

3.5
3
2.5
Shear Force

2
1.5
1
0.5
0
0 1 2 3 4 5 6
Load W

Experimental Theoretical

Figure 1 Shear force (N) vs Applied Load (W)

Table 2: Shear force(N) vs Applied Load (w) under different condition

Figure W1 (N) W2 (N) Exp RA RB Theoretical Error (%)

Shear (N) (N) Shear
force at Force at
cut (N) cut (N)
3 3.92 0 -1.3 5.162 1.247 1.242 4.67
4 1.96 3.92 3.3 2.67 3.20 3.474 5.01
5 4.91 3.92 2.3 2.58 6.24 2.31 0.433
 Shear Force (N) vs Applied load (W)
12

10
Shear Force (N)
8

0
0 2 4 6 8 10 12
Applied Load (W)

Figure 2 Graph of shear force for figure 5

Discussion
Experiment 1
The plot between theoretical and experimental values of shear force (N) vs applied load (w) is a
linear graph. This means that shear force is directly related to the applied load. But the graph of
theoretical and experimental values vs applied load is not directly overlapped. This might be due to
an error present in the experimental value. The sources of error include irregularities between
experimental values and inaccurate calibration of equipment. The sensitivity of the instrument is
also the possible reason for error because sensitive instruments are affected easily by their
surroundings. The maximum error of 13.64 % was observed in the case of 100gm mass. The error
can be eliminated by performing experiments repetitively and taking average values.

Experiment 2

The experimental measure and theoretical measure value of shear stress (N) at the cut position are
approximately closer to each other. The maximum percentage error (5.01) was observed in the case
of the figure (4). There was minimum error present in the condition given in figure 5.

Sources of error in both Experiment:

Possible sources of errors include the following.

 The movement of hangers by adding load can affect the experimental value.
 The sensitivity of the digital meter affects the reading.
 The movement of the beam during the experiment also affect the measured reading.
 The effect of surrounding on digital indicators can also affect the measured reading

Conclusion

Part 1 of this lab shows that the shear force (N) is directly related to applied load (w). The increasing
trend in shear force with applied load was the proof of a linear relationship. The second part of this
lab proved that shear force at the cut position is equal to the algebraic sum of all the applied loads.
The slighter error in the measured and experimental values are corresponding to the above-
mentioned error factor.
References

1. Beer, Ferdinand P.; E. Russell Johnston; John T. DeWolf, Mechanics of Materials.

Tata McGraw-Hill Education, 2004, pp. 322–323.
2. Frank Durka and Hassan Al Nageim, Structural Mechanics: loads, analysis, design
and materials (6/E). Longman Group, United Kingdom, 2002, pp. 45-65. Hibbeler, R.,
Statics and Mechanics of Materials (4/E). Singapore: Prentice Hall. (G. Seow, & J.
Wong, Eds.), 2013.
Appendix
Experimental set-up for the experiment

Figure 3 Apparatus Diagram

Figure 4 Part 1 Diagram for RA and RB Location

Theoretical Shear Force and percentage error for experiment 1.

W .a
Shear force=
l
For the mass 1. 100gm, 2. 200gm, 3. 300gm, 4. 400gm, 5. 500gm

0.98∗260
1. Shear force= = 0.579
440
1.96∗260
2. Shear force= = 1.158
440
2.94∗260
3. Shear force= = 1.737
440
3.92∗260
4. Shear force= = 2.310
440
4.91∗260
5. Shear force= = 2.901
440
¿
Percentage Error= ¿ ( Experimental−Theoretical )∨ Theoretical ¿ *100
Theoretical Shear Force and Percentage error for experiment 2.

The following equations were used to calculate the values of R A, RB and Shear Force.
Let; Ʃ MB = 0
(RA * L) +F(L-a) = 0

For Figure 3.
W1= 3.92 N
(RA * 0.44) + 3.92(0.140) = 0
RB= 1.247 N
RA= 3.92 +1.247
RA= 5.162 N
Shear Force= 3.92 – 5.162
= -1.242 N
¿
Percentage Error= ¿ ( Experimental−Theoretical )∨ Theoretical ¿ *100

¿
= ¿ ( 1.3−1.242 ) ∨ 1.242 ¿ *100

= 4.67 %

For Figure 4.
RA + RB= 5.88
RB(0.440)= 1.96(0.22) + 3.92(0.28)
RB= 3.474 N, RA= 2.405 N

Here shear force = 3.474 N

¿
Percentage Error= ¿ ( Experimental−Theoretical )∨ Theoretical ¿ *100

¿
= ¿ ( 3 .3−3.474 )∨ 3.474 ¿ *100

= 5.01 %

For Figure 5.

RA + RB= 8.82 N
RB(0.440)= 4.90 (0.24) + 3.92(0.40)
RB= 6.6236 N, RA= 2.556 N

Shear Force= -6.236+ 3.92

= -2.3164 N
¿
Percentage Error= ¿ ( Experimental−Theoretical )∨ Theoretical ¿ *100

¿
= ¿ ( 2.3−2.3164 )∨ 2.3164 ¿ *100
= 0.433 %