Civil Engineering

Civil Engineering

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Purpose of the Report

The aim of this task is to determine how much a loaded pin-jointed structure deflects experimentally, while comparing it with the deflection calculated theoretically, using virtual work.

Background (introduction)

Various forms of the plane trusses collectively are useful in structural components. Most engineers use the components in designing bridges and support structures. Ideally, they form an important part of most cranes (Doyle, 2001).

Structural engineers normally find the deflection of an individual joint of a truss by using the unit load method. The method bases its judgment on the Principle of Virtual Work. Most engineers normally compare the theoretical calculations of the deflection with the practical calculations. This helps in explaining the relationship that exists between the two approaches (Hamill,1998).

In this report, the experimenter determined the deflection of a loaded pin-jointed structure and compared the values with a theoretical deflection value calculated using a virtual work analysis. The main idea was to show a comparison between the structural model of the experimentally determined values and the idealized pin-jointed structure (Column Research Council, 1998).

Materials Used

Dial gauge, light tap, load hanger, loads of 20N, recording paper and pen.

Method and procedure

1. Ensure that the dial gauge is set in the right place. Use a light tap placed on the front of the gauge. The light tap is very important especially during the beginning of the experiment. The tap will assist in the reading of the increments after increasing the load amount.

2. Take the load hanger as a no load. This will help in recording the initial gauge reading; thus, an increase in the load will give a separate value from the initial reading.

3. Add an additional 20N load to the load hanger. This will give a new value separate from the initial value. Record the new reading showed on the gauge reading. From the theoretical perspective, an added load will apply a more than its static value thereby giving a new value.

4. Add additional loads in patterns of 20N until the load amounts to 100N. Record gauge readings on an individual increment of the load that is for every additional 20N record the new reading separately.

5. Reduce the load from 100N to zero. Ensure that the decrements are in 20N while recording individual readings after every decrement of 20N.

6. Enter the collected values in a table and calculate the average deflection that corresponds to each individual load: 20N, 40N, 60N, 80N, and 100N.

Results and discussion

Deflection Load (N)

0 0.001 0N

1 0.075 20N

2 0.140 40N

3 0.190 60N

4 0.230 80N

5 0.280 100N

6 0.001 After removing all the loads

From the above graph, it is clear that as the load increases, so is the deflection against the load. However, the initial position (the intercept) is not zero. From the result, it is evident that the truss behaved in a linear elastic manner.

Questions under discussion

1. Plot the deflections of joint G against the load. From the best fit, establish the deflection corresponding to a load of 100N.

2. Observe whether the truss behaved in a linear elastic manner or not.

3. Calculate the theoretical value of the deflection of joint G and compare it with the experimental value.

4. Discuss the findings.

Conclusion

From the result collected in the graph above, it is evident that as the load increases, the deflection of the joint against the load also increases. However, the graph shows an increasing rate of the deflection meaning that with an extra load, the elasticity of the loading arm will reduce leading to permanent elasticity. This explains the reason as to why the load should not pass past a certain load as permanent elasticity may prevail.

In comparing the theoretical calculation of the Euler, buckling load from the slope does not have a significant difference with the calculated value. This shows the accuracy of the experiment performed by the student.

Behavior of compression members

Purpose of the report

The experiment aims to investigate the behavior of loaded struts with initial curvature experimentally. It also aims to determine Euler buckling load experimentally by making use of Southwell plot.

Abstract

Background (introduction)

A steel bar withstands tensile stresses until the yield stress value. The yield stress value for the steel bar indicates the end of the elastic behavior and the beginning of plastic behavior. However, compressive stresses make structural elements fail to reach their yield stress value. The level at which these elements will fail when subjected to compressive stresses depends on their lengths and cross-section. A point in the case is a ruler, which is slender and will suddenly bow when subjected to a high stress level. This high stress level causes high instability to the ruler. This is referred to as buckling under the stress level. The original shape is regained for very long and thin elements after pressure from the compressive stressor is removed (Holt, 1951).

A strut that has initial curvature, which assumes the initial shape of the strut, can be described by use of a mathematical formula. The mathematical formula describes the relationship between the cross sectional area and the length of the element, with the maximum central amplitude of the structural element. A different formula is used to show the differential equation, which describes the elastic bending behavior when the compression load is applied on the element. This formula is d2(y-y0)/dx2= -M/E.I.