FACULTY OF ENGINBERING AND BUILT ENVIRONMENT
BEng (Hons) Civil Engineering
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:
Is to find the relationship between the deflection at the center of a simply supported beam and the span, width.
Frame with Movable Knife Edge Supports.
Steel rectangular beam.
I. We’ve arranged the beam span as 1000mm by locating the knife edges on the beam supports, then the mid span point has been measured, thus we were able to place the load hanger. II. We’ve measured the width and depth of the beam.
III. We’ve settled gauge by assuming the load hanger as zero load. IV. We’ve applied first 0.5N on the load hanger and recorded the first reading of the deflection by the dial gauge instrument. V. By adding 0.5N to the load hanger we were able to record the next readings. VI. Then we’ve taken off the loads and repeated the test.
VII. For the theoretical deflection we’ve got it from the formula: δ= WL3 / 48EI
By substitution W as (0.5N then 1N, until 2.5N)...
Span of the beam:
L = 1000 mm
Width of the beam:
b = 25 mm
Depth of the beam:
h = 6 mm
Thus Moment of inertia is: I = = 450
E = 200 GPa = 2 N/
Theoretical deflections are:
δ1= = 0.1157 mm
δ2= = 0.2314 mm
δ3= = 0.3472 mm
δ4= = 0.4629 mm
δ5= = 0.5787 mm
Theoretical deflection (mm)
Difference between theoretical and experimental deflections (mm)
Test (1) deflection
Test (2) deflection
Table 1 - Deflection at centre of a simply supported beam (mm)
Figure1 (Load VS Deflection)
From the results, it can be seen that the load and deflection are directly proportional. As the load is raised, the deflection also increases. Vice versa, when the load is removed, the deflection decreases as well, it can also be noted that the theoretical deflection is higher than the experimental deflection. This can be due to the errors committed during the lab work as well as the effect of limiting factors such as inaccuracy of readings for more than two decimal places. The percentage error is high and it proves that the experiment wasn’t done as cautiously as it should be. The theoretical value is very high in relation to the experimental values, the error can be observed in deflection when the load was being removed as it has a0.3mm reading when no load is placed. This could be due to the zero error which means that the arrow was not placed to zero before the experiment began or it could be due to some defects in the apparatus. It could also be due to air...
References: Mechanics of Materials, Russell C. Hibbeler
Experimental methods: an introduction to the analysis and presentation of data, By Les Kirkup
Mechanics of Materials (8th ed.), By Gere, James M., Goodno, Barry J.
Materials Science and Engineering an Introduction (4th ed.), William D Callister, JR
(Frank Durka and Hassan al Nageim, 2003)
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