LAB INVESTIGATIONS 2

shear force measurement of simply supported beam

Student Name: Yazid Ali SaeedStudent ID: SCM - 017278Date of submission: 4/11/2014Lecturer : Dr.LaiProgramme: B.Eng (Hons) Mechanical Engineering

OBJECTIVE

To show the shear force at a cut section of a beam is equal to the algebraic sum of the forces acting to the left or right of the section.

ABSTRACT

The purpose of this experiment is find shear force on beam and compare the values with algebraic and experimental. Taking a set of weights and measuring the lengths of the points and noting it down and them recording the experimental value from sensor , hence from the recorded values and can use them in Algebraic sum and then calculate forces . the values obtained , can be plotted in on a table . From the table , a bar chart can be obtained to find any significance or difference in the values and at last a conclusion on the experiment and how accurate it is.

THEORY/INTRODUCTION

Due to applied loads on the beam, it develops an internal resisting shear force that at any section of beam is equal to the algebraic sum of external forces. Shear force may be defined as the algebraic sum of all the external forces either to the left or right of a section.

To obtain shear force values, we have to take section at various prominent points over the beam. Moving from right to left, we find point just to the left of support (there is no use in taking section right on the support).

APPARATUSA pair of simple supports, A steel beam with a cut section, a set of weights with several load hangers, Measurement apparatus (ruler, caliper, divider, etc).

Figure1. Appratus for measuring Shear force

Figure 2 .A sensor reader is used to get the reading from sensor

Figure 3. weight in newtons

PROCEDURES1. Connected the digital indicator to the transducer and switched on the indicator.2. For stability of the reading, the indicator must be switched on 10 minutes before taking readings.3. Hung the three load hangers to the beam and noted down the reading of the location of the load hangers, i.e. L1, L2 and L3.4. Recorded down the indicator readings. Pressed the tare button on the indicator so that the reading is zero.5. Placed a desired load on each load hanger and recorded the value W1, W2 and W3.6. Recorded down the indicator reading. This represents the shear force at the cut section.7. Removed all loads from the load hangers and repeat step 4 7 for another 5 different sets of loading condition.

RESULTS

Free Body Diagram of beam

Free Body Diagram for a Cut section

Weight of the loads RA (N)RB (N)Bending Moment, M (Nm)Shear Force, V Digital Reading ()Theoretical Shear, V()

W1

W2

W3

55510.344.651.164.664.66

105515.214.781.745.35.37

1010518.146.851.716.846.85

10101020.699.302.329.289.30

1051519.7310.272.5710.310.27

552018.0111.983.0012.0411.98

Table 1

Figure 6. Digital Shear force vs Theoretical Shear force

CALCULATION Below are some Algebric formulas that can be used to calculate the given forces

To find RB by using equation ,As W1, W2 and W3 = 5 n-RB (0.93) + W1 (0.135) + W2 (0.275) + W3 (0.455) = 0

To find RA by using equation , RA + RB -W1 W2 W3 = 0

To find M by using equation ,RA (0.68) W1 (0.68-0.135) W2 (0.68-0.275) W3 (0.68-0.455) M = 0

To find shear force,V by using equation ,=>RA + V -W1 W2 W3 = 0

DISCUSSIONComparison and difference in the theoretical and experimental is not much , the values are almost same and it can be concluded that the experiment went successful without much errorsThe use of shear force diagram is to understand the structural of the system and hence any forces acting on the beam can be easily calculated and other factors can be also resolved.The experiment is very accurate as there is less difference in the values compared .For improvement of the experiment that can be done is to use better beam on the system and better sensor that can avoid unnecessary readings that could affect the values.

CONCLUSION From this experiment we can conclude that it went successful and more accurate .Algebraic sum of values and experimental values are almost same and it can be concluded that we can use Algebraic sums to figure out the forces in a given system.

References1. Google Images( Apparatus )2. Ronald D., 2005, Structural foundation3. C. Martin, D. R. Croft 2001, Martial loadings ,