Cantilever Beam Load, Bending Moment, Stress and Strain, Slope and Deflection
Cantilever Beam
Table of Contents
Table of Contents 2 1. Introduction 3 2. Theory 3
2.1 Bending Moment and Stresses 3
2.2 Deflection and Slopes 5 3. Equipment 6 4. Procedures 7
4.1 Procedure 1 7
4.2 Procedure 2 8
4.3 Procedure 3 8 5. Results 8
5.1 Results from procedure 1 8
5.2 Results from procedure 2 10
5.3 Results from procedure 3 12 6. Discussion and Error Analysis 14 7. Conclusion 15
1. Introduction
During this lab a beam was tested in order to find the relationships between load, bending moment, stress and strain, slope and the deflection in a cantilever beam which was the main objective.
The main purpose was to understand the fundamental principles that have to be taken into account before designing and manufacturing a beam or using one as part of a design.
2. Theory
The theory behind this lab can be categorized to 2 different topics, bending moment and stress being the first, the second being slope and deflection. Each one is discussed below: 2.1 Bending Moment and Stresses
Picture [ 1 ]
Bending moment is a moment produced by a load applied on a surface that causes it to bend. In the case of the lab the surface is the beam and with the applied at the end of it. In order to calculate the bending moment it is necessary to draw a Free Body Diagram indicating all the forces applied upon the beam.
Picture 1 is the free body diagram of the beam. F is the load applied, R is the reaction from the clamps (the bar is fixed on the bench by two G clamps) and M is the bending moment. Since we need to have equilibrium and no forces on the x-axis there are two equations we should use the following equations:
If we resolve the vertical forces for the whole beam
ΣFY=0↔F-R=0 ↔ F=R (1)
By taking moments anti-clockwise about right hand side for the whole beam WL+ M=0 ↔ M=-WL (2)
Equation (2)
Table of Contents
Table of Contents 2 1. Introduction 3 2. Theory 3
2.1 Bending Moment and Stresses 3
2.2 Deflection and Slopes 5 3. Equipment 6 4. Procedures 7
4.1 Procedure 1 7
4.2 Procedure 2 8
4.3 Procedure 3 8 5. Results 8
5.1 Results from procedure 1 8
5.2 Results from procedure 2 10
5.3 Results from procedure 3 12 6. Discussion and Error Analysis 14 7. Conclusion 15
1. Introduction
During this lab a beam was tested in order to find the relationships between load, bending moment, stress and strain, slope and the deflection in a cantilever beam which was the main objective.
The main purpose was to understand the fundamental principles that have to be taken into account before designing and manufacturing a beam or using one as part of a design.
2. Theory
The theory behind this lab can be categorized to 2 different topics, bending moment and stress being the first, the second being slope and deflection. Each one is discussed below: 2.1 Bending Moment and Stresses
Picture [ 1 ]
Bending moment is a moment produced by a load applied on a surface that causes it to bend. In the case of the lab the surface is the beam and with the applied at the end of it. In order to calculate the bending moment it is necessary to draw a Free Body Diagram indicating all the forces applied upon the beam.
Picture 1 is the free body diagram of the beam. F is the load applied, R is the reaction from the clamps (the bar is fixed on the bench by two G clamps) and M is the bending moment. Since we need to have equilibrium and no forces on the x-axis there are two equations we should use the following equations:
If we resolve the vertical forces for the whole beam
ΣFY=0↔F-R=0 ↔ F=R (1)
By taking moments anti-clockwise about right hand side for the whole beam WL+ M=0 ↔ M=-WL (2)
Equation (2)