Stress Analysis Report

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  • Topic: Shear stress, Second moment of area, Beam
  • Pages : 15 (4347 words )
  • Download(s) : 242
  • Published : July 9, 2012
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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 occur depending on how the strain gauge deforms and a voltage is measured.

The data collated from the experiment was then processed and the determination of stress distributions was completed in 3 ways; analytically, then graphically using a Mohr’s strain circle representation and finally a Finite Element Analysis (FEA). This models the aluminium body simulating the effect of the load on the structure and instantaneously calculates the stresses and strains along the beam.

2. Materials and Methodology

2. 1 Materials

The Instron material test machine was used to complete the 4 point bending test on the aluminium beam. In actual fact the “yellow dot” beam was tested and was actually 49.96 by 24.86 mm. Fig 1.1 shows how the beam was tested and shows the positions of the loads applied and the supports on the beam. The downward deflection of the aluminium alloy beam was limited, to keep within the ranges of the strain gauges and the elastic limits of the beam. A 4-point bending rig was set up rather than a 3-point bending rig

The signal processing Madaq 16 software was prepared and all 14 input channels were selected. These channels are the 14 strain gauges than were connected on to the beam. One was places above the beam and the other was placed below the below at the exact same axial location. As mentioned before the other 12 strain gauges were compiled in 4 strain gauge rosettes.

Figure 2.1: Photo showing the positions of strain gauges 1 to 6, the first 2 strain gauge rosettes

Figure 2.2: Photo showing the positions of strain gauges 7 to 12, the 3rd and 4th strain gauge rosettes

As the beam deforms, the strain gauge also deforms. This deformation of the strain gauge causes the electrical resistance to the increase, and since each gauge carries an electric current values of voltage are displayed on the Madaq 16 programme. The rosettes were arranged in sets of 3 in order to measure the orthogonal direct strains, in the x and y direction, and the...
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