Beam Deflection Experiment
1.0 BACKGROUND OF STUDY
The deflections of a beam are an engineering concern as they can create an unstable structure if they are large. People don’t want to work in a building in which the floor beams deflect an excessive amount, even though it may be in no danger of failing. Consequently, limits are often placed upon the allowable deflections of a beam, as well as upon the stresses.
When loads are applied to a beam their originally straight axes become curved. Displacements from the initial axes are called bending or flexural deflections. The amount of flexural deflection in a beam is related to the beams area moment of inertia I, the single applied concentrated load P, length of the beam l, the modulus of elasticity E, and the position of the applied load on the beam. The amount of deflection due to a single concentrated load P, is given by δ=PL3kEI whereby k is a constant based on the position of the load, and on the end conditions of the beam.
The bending stress at any location of a beam section is determined by the flexure formula, σ=MyI whereby M is the moment at the section, y is the distance from the neutral axis to the point of interest and I is the moment of inertia.
2.0 OBJECTIVES
2.1 EXPERIMENT 1
To investigate, for a simply supported beam carrying a central point load, a) The relationship between the deflection and the applied loads b) The effect of variations in length and cross sectional dimensions on the beam compliance
2.2 EXPERIMENT 2
To investigate, for a cantilever beam carrying an end point load, a) The relationship between the deflection and the applied loads b) The effect of variations in length and cross sectional dimensions on the beam compliance
2.3 EXPERIMENT 3
To investigate, for a simply supported beam subjected to a uniform bending moment, the effect of variations in length over which the beam is supported.
3.0 PROCEDURES
3.1 EXPERIMENT 1
Simply Supported Beam with Central Point Load
Figure 3.1 Set-up for
The deflections of a beam are an engineering concern as they can create an unstable structure if they are large. People don’t want to work in a building in which the floor beams deflect an excessive amount, even though it may be in no danger of failing. Consequently, limits are often placed upon the allowable deflections of a beam, as well as upon the stresses.
When loads are applied to a beam their originally straight axes become curved. Displacements from the initial axes are called bending or flexural deflections. The amount of flexural deflection in a beam is related to the beams area moment of inertia I, the single applied concentrated load P, length of the beam l, the modulus of elasticity E, and the position of the applied load on the beam. The amount of deflection due to a single concentrated load P, is given by δ=PL3kEI whereby k is a constant based on the position of the load, and on the end conditions of the beam.
The bending stress at any location of a beam section is determined by the flexure formula, σ=MyI whereby M is the moment at the section, y is the distance from the neutral axis to the point of interest and I is the moment of inertia.
2.0 OBJECTIVES
2.1 EXPERIMENT 1
To investigate, for a simply supported beam carrying a central point load, a) The relationship between the deflection and the applied loads b) The effect of variations in length and cross sectional dimensions on the beam compliance
2.2 EXPERIMENT 2
To investigate, for a cantilever beam carrying an end point load, a) The relationship between the deflection and the applied loads b) The effect of variations in length and cross sectional dimensions on the beam compliance
2.3 EXPERIMENT 3
To investigate, for a simply supported beam subjected to a uniform bending moment, the effect of variations in length over which the beam is supported.
3.0 PROCEDURES
3.1 EXPERIMENT 1
Simply Supported Beam with Central Point Load
Figure 3.1 Set-up for
References: [1] GERE, J.M. (1998). Axially Loaded Members, Mechanics of Materials. 3rd S.I. Ed. Cengage Learning, 53p – 55p. [2] BEER, F.P. (2006). Deflection of Beams, Mechanics of Materials. 4th S.I. Ed. McGraw-Hill, 533p – 537p, 542p. [3] Beam Deflection Apparatus, The Sanderson Range of Mechanical Engineering Laboratory Apparatus. [4] http://www.clag.org.uk/beam.html