Bending Moment in Beam Section Essay Example

the desired location.

Results

Beam span= 800 mm
Distance of the cut section from the right support= 300 mm
Distance of the load cell from the centre of the beam cross section= 175 mm

Using the date in the Table above plot the bar chart for the bending moment for the theoretical and experimental case for each load case. Calculate the percentage error for each load case and hence determine the overall percentage error. Percentage error= ((slope theory – slope exp) / (slope theory)) x 100 %

• Case 1 : Percentage error= ((1462. 5 – 1440. 25) / 1462. 5 ) x 100 % = 1. 52 %
• Case 2 : Percentage error= ((2156. 25 – 2124. 5) / 2156. 25 ) x 100 % = 1. 47 %
• Case 3 : Percentage error= ((2587. 5 – 2677. 5) / 2587. 5 ) x 100 % = -3. 48 %
• Case 4 : Percentage error= ((3437. 5 – 3473. 75) / 3437. 5 ) x 100 % = -1. 05 %
• Case 5 : Percentage error= ((4175 – 4287. 5) / 4175 ) x 100 % = -2. 63 %
• Overall percentage= ((13818. 75 – 14003. 5) / 13818. 75 ) x 100 % = -1. 34
  

%

Discussion

What actually happens when a load is applied to the beam and why does this condition occur. When a load is applied to the beam, it beads in a downward direction like a curve. Bending is the behaviour of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. It caused the inside of the curve to compress (shortened) while the outside of the curve to tense (pulled apart). This condition occurred because new forces are imposed along the length of the beam when the beam bends. The beam experiences a bending moment hence changed its shape and internal stress (force) is developed.

There are two forms of internal stresses caused by lateral loads, shear stress and direct compressive & direct tensile stress. The amount of bending deflection and the stresses that develop are assumed not to change over time. The forces form a couple of moments as they are equal in magnitude and opposite in direction. This bending moment resists the sagging deformation characteristic of a beam experiencing bending.

Will the readings of the load cell differ from the above if it is placed at 100mm from the centre of the cross-section. If your answer is yes by how much.

If your answer is no, then why. The readings of the load cell will not be differed from the experimental reading if it is placed at 100mm from the centre of the cross-section. This is because the bending of a beam depends on the beam’s load, material properties, cross-section, and manner of support, but not the length or distance of load to the support. Eventually, a change in the

length of the loads would not affect the readings of the load cell. There might be a slight difference in the reading that is caused by human error or the surrounding’s factor but still, it would not change the result of the experiment.

In this experiment, we can place the loads anywhere within the two supports. Comment on the accuracy of the experiment. According to the results we obtained, the percentage difference of the experimental value and the theoretical value of the load cells in each case has not more than 5%. For the overall percentage difference, it only has a difference of -1. 34%. The results shown have determined the accuracy of the experiment which is quite accurate and it can be said that this experiment is suitable to be carried out to determine the bending moment at a cut section of a beam.

State the probable factors that affect the accuracy of the experiment.

Human error. The human error took place during reading, such as parallax error, which might have contributed to the discrepancies in the final results. The rings which we used to hang the load hangers should be placed with careful accuracy when the eye is perpendicular to the reading apparatus (the top of the beam has measurements to place the rings on the desired length).

Friction forces. Frictions at the joints might have also caused slight deviations in the reading, causing deviation and inaccuracy in the readings. c) Device sensitivity * The digital indicator is a very sensitive device. It can detect any minor movement and therefore affect the accuracy of the readings. To increase the accuracy of the readings, we have to place

the loads simultaneously once the tare button (which caused the reading to reset to zero) is pressed.

Conclusion

As what we obtained in the results, the overall percentage difference of the experimental value and the theoretical value of the load cell is -1. 34%. The bending of a beam depends on the beam’s load, material properties, cross-section, and manner of support.

We have learned a great deal about how the bending of a beam depends on the beam's load, material properties, cross-section, and manner of support. Engineers use the static beam equation and the ideas that we have explored as a basis for understanding the static deformations of more complicated structures. As you have seen, integration plays a key role in an engineer's ability to analyze these structures. What we have not yet addressed, however, is an important mathematical feature of the static beam equation that helps engineers to approximate real loads by examining combinations of the idealized loads that we have been studying.

The important observation is that the static beam equation is a linear differential equation. Of the many important characteristics of linear differential equations, the one we will be concerned about is called linearity of solutions. For us, this means that if we know how a beam bends under the load distribution q(x) and we also know how the beam bends under the load distribution, p(x), then we also know how the beam bends under the loads q(x) + p(x), q(x) + 2 p(x), -q(x)+0. 3 p(x), and, in fact, any load that may be expressed as A q(x) + B p(x) for some numbers A and B.