# Shear Force Acting on Beams

MS&E- 04

Abstract:

In this experiment we come to know how different amalgamation of loads and distances causes the variation of bending moments across the length of a beam. Another attribute of this report is that it envisage about the agreement of theoretical values calculated with those which are calculate during the experiment. The experiment was designed to foster creative thinking and to make the study of structural analysis more meaningful by incorporating the concept of design, model, test, observe and discuss.

Regards Muhammad Zia ul haq MS&E- 04

Theory:

Firstly, to compare the theoretical internal moment with the measured bending moment for a beam under various loads, and Secondly, to measure the shear force at a normal section of a loaded beam and to check its corroboration with theory. The basis of this experiment is to give students a hands-on experience and give them an idea of structural analysis and its application in Material Science and Engineering through real-life examples such as bridges, etc. This experiment bears exemplary significance in the careers of Material Students as it integrates Material Analysis, Stress Analysis, Structural Study, Force Application and Theoretical Calculations. Normally a beam is analysed to obtain the maximum stress and this is compared to the material strength to determine the design safety margin. It is also normally required to calculate the deflection on the beam under the maximum expected load. The determination of the maximum stress results from producing the shear and bending moment diagrams. To facilitate this work the first stage is normally to determine all of the external loads.

Figure 1 Shear force acting on Beams

Typical Diagrams

A shear force diagram is simply constructed by moving a section along the beam from (say)the left origin and summing the forces to the left of the section. The equilibrium condition states that the forces on either side of a section balance and therefore the resisting shear force of the section is obtained by this simple operation. The bending moment diagram is obtained in the same way except that the moment is the sum of the product of each force and its distance(x) from the section. Distributed loads are calculated buy summing the product of the total force (to the left of the section) and the distance(x) of the centroid of the distributed_load. The sketches on the next page show simply supported beams with on concentrated force.

Figure 2

Shear Force Diagram

Shear force diagrams are simply plots of the shear force (on the y-axis) versus the position of various points along the beam (on the x-axis). Thus, the following is the generalized shear force diagram for the beam shown above.

Figure 3

The shear force diagram indicates the shear force withstood by the beam section along the length of the beam. It is normal practice to produce a free body diagram with the shear diagram and the bending moment diagram position below For simply supported beams the reactions are generally simple forces. When the beam is built-in the free body diagram will show the relevant support point as a reaction force and a reaction moment.

Figure 4

Experimental Construction:

Fix the beam supports permanently to provide a span of 900mm. Make a pencil mark on the side of the beam 300mm from the phase of the shear section. Use this to postion the beam on its supports. Make pencil marks on top of the beam at 100mm...

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