Stress Analysis Report
1. Introduction
The aim of this experiment was to study the behaviour of a beam subjected to increasing bending moments and to discover the stress distribution in the beam for both the direct and shear stresses. This was done by applying a known load to the beam and recording the deflection of the loading points. These readings were then analysed to give the axial direct strains and stresses as well as the shear strains as stresses at the sites of the strain gauges. As a result, the stress distribution of the beam can be calculated.
The aluminium alloy beam was tested and had a nominal cross-section 50 mm deep by 25 mm wide and was loaded on the 25 mm face. The beam was subjected to a “4-point bending” system to increasing loads up to 8 kN. The beam was experimented using an Instron testing machine, which applied two equal loads at two different points along the beam. A four point bending setup was carried out instead of a three point bending setup as a three point bending test rig has just maximum bending moment at one location which makes it difficult to place a single strain gauge at this precise position. On the other hand, with a four point bending test rig experiment can be made more accurate as strain gauges can be evenly spaced in the region of constant bending moment where the shear stress is zero in the four point bending rig.
0.3 m
0.4 m
0.3 m
4 kN
4 kN
50 mm
25 mm
0.3 m
0.4 m
0.3 m
4 kN
4 kN
50 mm
25 mm
Figure 1.1: Diagram showing the representation of the Instron testing rig
Figure 1.1 above shows a schematic of how the aluminium beam was set up during the experiment on the Instron materials test machine. There are 14 strain gauges that were attached to the beam. Two strain gauges were positioned on the top and bottom surfaces of the beam at the same axial location. The other 12 strain gauges were connected in sets of 3, called strain gauge rosettes. The gauge carries an electric current and changes in electric resistance
The aim of this experiment was to study the behaviour of a beam subjected to increasing bending moments and to discover the stress distribution in the beam for both the direct and shear stresses. This was done by applying a known load to the beam and recording the deflection of the loading points. These readings were then analysed to give the axial direct strains and stresses as well as the shear strains as stresses at the sites of the strain gauges. As a result, the stress distribution of the beam can be calculated.
The aluminium alloy beam was tested and had a nominal cross-section 50 mm deep by 25 mm wide and was loaded on the 25 mm face. The beam was subjected to a “4-point bending” system to increasing loads up to 8 kN. The beam was experimented using an Instron testing machine, which applied two equal loads at two different points along the beam. A four point bending setup was carried out instead of a three point bending setup as a three point bending test rig has just maximum bending moment at one location which makes it difficult to place a single strain gauge at this precise position. On the other hand, with a four point bending test rig experiment can be made more accurate as strain gauges can be evenly spaced in the region of constant bending moment where the shear stress is zero in the four point bending rig.
0.3 m
0.4 m
0.3 m
4 kN
4 kN
50 mm
25 mm
0.3 m
0.4 m
0.3 m
4 kN
4 kN
50 mm
25 mm
Figure 1.1: Diagram showing the representation of the Instron testing rig
Figure 1.1 above shows a schematic of how the aluminium beam was set up during the experiment on the Instron materials test machine. There are 14 strain gauges that were attached to the beam. Two strain gauges were positioned on the top and bottom surfaces of the beam at the same axial location. The other 12 strain gauges were connected in sets of 3, called strain gauge rosettes. The gauge carries an electric current and changes in electric resistance
References: 3. Amis, A: ME2 Stress Analysis, 2011-2012, Imperial College London 7