# Mechanics of Materials — Lab Report Essay Example

Comment on the shape of the graph. What does it tell us about how angle of deflection varies because of an increase torque? Name at least three applications or situations where torsional deflection would be undesirable

Results from the beam bending experiment

T he figure above indicates the relationship between the deflections vs. the force applied in all the five beams. It is evident that steel is the strongest beam. The beam deflects at a very small level once the maximum force is applied. Aluminum is the second strongest beam cantilever that deflects very minimal than the aluminum box beam which follows in terms of strength. Basswood beam is the fourth strongest because it deflects at a very huge rate at a small effort. Polystyrene is the last beam. It deflects immensely at a very small effort.   Considering the fact that the gradient of the graph m is 28.789 that starts from the origin and then intercept at zero

The rod length is directly proportional to angular deflection.

This graph can be summarized as  (θ )= kL

Whereby Constant k=(T/JG0-28.789rads/m that is the gradient

L=rod variable length

K=constant

ϴ=deflection angle

The shock on the diameter and the length has considerable influence on the returning outcome of the transmitted torque through the shafts. Specifically, there is a point that the shaft bends into an s shape whenever the speed stated exceeds. However, the shorter lengths and smaller diameters of the shafts produce low torques and low speed critical limit if it exceeds. If the diameter is short and small than the shafts, this shall mean that there will be a critical speed limit and low transmission. If the speed limit exceeds this shall cause a failure of the shaft. This theory relates to the stiffness of the Torsional T=JG(ϴ/L) because the length is inversely proportional to the torque where the shaft torque is directly proportional to the diameter.

Take a look at the formulas on the backboard that predicts the behavior of the rods. What would happen to the stiffnesss of the rod if the diameter were increased from 3mm to 4mm? How would your graph change if the rod was made of brass knowing that its shear modulus of elasticity is about half that of steel.

The main comparison in this case of the hollow brass and brass rod therefore resulting information that is insurmountable concerning the selection of the hollow shaft or the solid shafts. As per the results indicated the outcome of the solid brass and the hollow brass closely have an equal output stiffness and torque output. Considering the graph on the angular deflection verses the torque of the solid brass rods (brass tubes and brass rods) therefore there is a considerable in the level of gradient. From stiffness and torque, T=JG(ϴ/L)

The equation is y=mx+c (L/JG) is the gradient

ϴ is the angular deflection

T=Torque

For the hollow and rod shats the gradient will be m with a neglible comparison of (3 vs 4)

The comparison graph of brass tube and brass rode, the gradient are 0.0033 vs 0.0034 this indicates a very small difference between hollow and solid shafts. This small difference arises from the small difference because of the power 4 factors. Therefore it would be recommendable and economical to apply the hollow shafts unlike the solid shafts because they have the same stiffness torque. Hollow shafts are cheap because they consume less materials.

Plot the graph of TL against Ip. Examine the torsion formula and say what the values of the gradient represents. Does the values compare favourably with typical ones?  Write down all required information such as the dimensions of the beam From your results, plot a graph of strain against bending moment for all nine gauges Discuss how these graphs would change if the beam material had a modulus of elasticity of one third of that of aluminum Also draw the shear force and bending moment diagrams of the beam. Locate the neutral axis and calculate the second moment of area beam. Predict the bending stress and straight at the location of strain gauges and indicate where they are positive or negative. Discuss any discrepancy between your theoretical and experimental results.  The value of the shear force need to be plotted This values can be plotted

The Bending Moments will be

What is the relationship between the bending moment and the strain at the various positions?

The cross section distance when the beam bends x from the lest side will be obtained from a free body C1 is constant

This equation can be intergrated to be 