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.
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
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
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.
Simply Supported Beam with Central Point Load
Figure 3.1 Set-up for Experiment 1
Test| l (mm)| b (mm)| d (mm)|
1| 350| 21| 6|
2| 550| 21| 6|
Table 3.1 Beam Deflection Setting for Experiment 1
1. A rectangular beam is prepared with the length l of 600mm, base b of 21mm and height h of 6mm. 2. The two hardened knife edge support beams are set up which is attached with the beam deflection apparatus in a span of 375mm in dimensions. 3. The beam on the support beam is placed.
4. A dial gauge is attached to the beam deflection apparatus and is placed in the middle of the beam and fastened to the apparatus. 5. The dial gauge support is allowed to slide freely on the beam. 6. The dial gauge is selected to a fixed point where the deflection is to be measured later. 7. A load of 100g is placed in the middle of the beam.
8. The result of the deflection from the dial gauge is checked and the measurements are collected in a table. 9. The methods above are repeated by adding 100g weight w until the total load reaches 500g. 10. For Test 2, the span of the beam of 550mm in dimensions is adjusted using the same beam. 11. The methods above are repeated beginning with a load of 100g weight w until the total load reaches 500g. 12. The effect of decreasing l is written and compared to Test 1 and Test 2.
Cantilever Beam with End Point Load
Figure 3.2 Set-up for Experiment 2
Test| l (mm)| b (mm)| d (mm)|
1| 300| 21| 6|
2| 450| 21| 6|
Table 3.2 Beam Deflection Setting for Experiment 2
1. A rectangular beam is prepared with the length of 600mm, base b 21mm and height h 6mm. 2. The beam is placed in a cantilever support with the length l of 300mm from one end of the beam to the cantilever support. 3. The beam is clamped tightly to the cantilever support. 4. A dial gauge is attached to the beam deflection apparatus which is placed at the end of the beam and fastened to the apparatus. 5. The...