FACULTY OF CIVIL ENGINEERING & EARTH RESOURCESSTRUCTURE LABORATORY

SUBJECT CODE

BAA 2921

SUBJECT

ENGINEERING LABORATORY II

EXPERIMENT TITLE

REACTIONS AND FIXING MOMENT OF A FIXED BEAM AND A PROPPED CANTILEVER

DATE OF EXPERIMENT

17TH SEPTEMBER, 2013

GROUP NUMBER

3

SECTION

01

GROUP MEMBER:ID NUMBER AND NAME1. AA12107 INTAN NURSYAFIQAH BINTI MOHAMED HISSAM2. AA12113 FOO YUEN KEI3. AA12115 NURNAZIRAH BINTI MUHAMAD RAMZI4. AA12163 NURSALAM BIN ZAINAL

PERSON IN CHARGE

EN. MOHD BADWI BIN YUNUS

REMARKS

ENDORSEMENT

TABLE OF CONTENT

TITLE

PAGE

1.0INTRODUCTION/PRINCIPLES

2.0 OBJECTIVE

3.0 APPARATUS

4.0 PROCEDURE

5.0 RESULT

6.0 DISCUSSION/ANALYSIS

7.0 CONCLUSION

8.0 REFERENCES/APPENDIX

1.0 INTRODUCTION/PRINCIPLESINTRODUCTIONIn this experiment, fixed beam and propped cantilever beam are in use to do comparison related to moment and reaction.Fixed beam, is also known as built-in or encastre beam. The end of fixed beam always constrained in order to ensure the beam is always remains in horizontal position. To fulfil the condition of zero slope at each end, a fixidity moment will be induced at each end. Hence, a fixed beam is a statically indeterminate beam of second order due to the number of unknown reaction is more than equations that derives from static equilibrium.Propped cantilever beam, is a cantilever beam simply supported at one end, while another end is free. Normally, another free end is supported by roller or knife edge. This type of beams is external indeterminate beam of the first order. There are four reactions develop at the two supports of the beam and only three equations of equilibrium are available for analysing.

PRINCIPLESStatically determinate body, the equilibrium equations of statics are sufficient to determine all unknown forces or other unknowns that appears in equilibrium equations. Whereas statically indeterminate body the equilibrium equations of statics are not sufficient to determine all unknown forces or other unknown.The equilibrium equations in 2-D is given by: F = 0:The sum of the horizontal components of forces equals zero. F = 0:The sum of the vertical components of forces equal zero. M =0:The sum of moments (about the arbitrary point) of all forces equal zero.A simple rule of thumb to help ascertain whether an object is statically determinate or indeterminate is to compare the number of unknowns to the number of equilibrium equations. If n < 3 The body is statically determinate and it can have partial or no fixity.If n = 3The body is statically determinate if it has full fixity but indeterminate if it has partial fixity.If n > 3 The body is statically indeterminate and it can have full fixity or partial fixity.The equipment is used to investigate two beam arrangements as shown in Figure 1 below :

The indeterminate beams experiment fits into a test frame. Figure 3 shows the indeterminate beams experiment in the frame with loads and a digital force display to measure the applied forces.Before setting up and using the equipment, always : Visually inspect all parts, including electrical leads, for damage or wear. Check electrical connections are correct and secure. Check all components are secure and fastenings are sufficiently tight. Position the Test Frame safely. Make sure it is on a solid, level surface, is steady, and easily accessible. Never apply excessive loads to any part of equipment.

2.0 OBJECTIVE1. To determine the fix moment value for the fixed and propped cantilever beam.

3.0 APPARATUSThe equipment needed to perform this experiment:i. The backboard unit set up in the test frame

ii. The knife-edge and encastre fixing, load cell support

iii. A digital forcemeter with leads

iv. The thin flexible beam

v. A set of weight, weight hanger and a knife-edge hanger

1. The load cell support is put onto the test frame and it is slid to the 400mm position. It is fixed securely with two screws on the front only. The top clamp plate is removed from the load cell leaving the bottom plate in position.4.0 PROCEDURE

2. The screw is left loose, using the hole at one end secure the beam to the moment chuck on the backboard. The moment arm locking screw is undo to allow the beam to rest fully on the load cell. The beam in the load cell is clamped evenly and squarely with the two screw and clamping plate. The chuck screw and moment arm locking screw are tightened.

3. The moment arm is connected to input 1 and the load cell to input 2 on the digital force display. Each reading is selected in turn and the relevant control is used to zero the readings on the digital force display.

4. The left-hand end of beam is set to measure fixing moment and right-end is set to measure the support reaction.

5. A mass of 4.9 N is applied to the beam 40mm from the left-hand end. Readings of the moment arm force and support reaction force are taken and recorded in Table 1. The experiment is repeated in 40mm increments across the span of the beam. The moment MA is calculated by multiplying the moment arm force with moment arm length.

6. The moment arm clamp screw is released and the clamp screw on the load cell support is undo. Both clamp plates are removed from the load cell support to expose the knife edge. The beam is rested back onto the knife-edge and the moment arm clamp screw is tightened. By using the set zero control, both moment arm and the load cell support are set zero. Propped cantilever beam is set using the equipment.

7. The experimental procedure was repeated and used on the fixed beam for propped cantilever. The result was recorded in Table 2. The both set results were plotted fixing moment and vertical reaction versus position along the beam.

8. Theoretical values of all the moments and reactions are calculated using the equations provided in Figure 2.

5.0 RESULTS ExperimentalTheoriticalAccuracy(%)

Distance A (m)Load W (N) Moment Arm Force (N)MA (Nm)RB (N)MA (Nm)RB (N)MA (Nm)RB (N)

0.044.92.70.1350.20.1590.13715.0945.99

0.084.94.60.230.60.2510.518.3717.65

0.124.95.30.2651.20.2881.0587.9913.42

0.164.95.20.261.80.2821.7257.804.35

0.204.94.40.222.50.2452.4510.202.04

0.244.93.30.1653.20.1883.17512.230.79

0.284.920.13.90.1243.84219.351.51

0.324.90.80.044.40.0634.3936.500.23

0.364.9004.70.0184.763-1.32

Table 1: Result for Experiment 1 (Fixed Beam)

Table 2: Result for Experiment 2 (Propped Cantlever Beam)ExperimentalTheoriticalAccuracy

Distance A (m)Load W (N) Moment Arm Force (N)MA (Nm)RB (N)MA (Nm)RB (N)MA (Nm)RB (N)

0.044.93.50.1750.10.1680.074.1742.86

0.084.95.90.2950.30.2820.2754.619.09

0.124.97.10.3550.60.350.5951.430.84

0.164.97.60.3810.3761.021.061.96

0.24.97.40.371.60.3681.530.544.56

0.244.96.60.332.10.3292.1180.300.85

0.284.95.30.2652.80.2682.761.121.45

0.324.93.60.183.50.1883.454.261.45

0.364.91.70.0854.20.0974.16812.370.77

Calculations Example:MA = Moment Arm Force x 0.05Fixed Beam: MA = 2.7 x 0.05= 0.135Nm Propped Cantilever Beam:MA= 3.5 x 0.05= 0.175Nm6.0 DISCUSSION/ANALYSISi. Comment on the accuracy of your result. Compare the fixing moments and theoretical deflections for the propped cantilever and the fixed beams. What is the relationship between the experimental and theoretical values obtained?According to the graph, experimental results share the same graph shape with theoretical value. However, the value obtained from experiment is slightly different to theoretical values calculated. For fixed beam, the moment increases until it reaches 0.12m, the maximum point. Then, the moment decreases till 0.36m. For propped cantilever beam, the moment increases with the increment of distance till it reaches 0.16m. then moment starts to reduce till 0.36m. Next, the support reaction for fixed beam increases when distance increases. This goes similar to cantilever beam. Both beam reach maximum point at 0.36m. Theoretical values obtained are the value of structure in ideal condition as assumption. Hence, the differences in experimental values affect the accuracy of the result.

ii. Are the equations that describe the support reactions derived from static equilibrium? If not why? Find a method to derive the equations for the beam. Yes. The equation is derived from static equilibrium. For fixed beam, there is 6 unknown forces and propped cantilever beam has 4 unknown forces. Using equilibrium equations, let the summation of the components from different direction equal to zero. By using such method, the equations for beam are obtained.

iii. Give advantages and disadvantages for using a fixed beam or a propped cantilever for a simple bridge.Fixed BeamPropped Cantilever Beam

Advantages More stable because it has both side fixed and supported. One end fixed, another end can be supported using roller or pin. Easier for bridge to expand during hot weather.

Disadvantages Only suitable for short range bridge. The bridge will deflect when expand during hot weather. Less stable than fixed beam. Need high strength material to support load.

iv. If it is needed to draw load versus MA and RB, explain how the experiment procedure will be changed and explain how to obtained critical load from the graph?To draw load versus MA and RB, distance A becomes constant variables. The values of load will be affected by the value of MA and RB, load is then become the responding variables. Theoretically, Moment = Distance x Reaction of force. Hence, 1/Distance = Reaction of force/Moment. From gradient, we can obtain the critical distance.

v. What are the precautions that should be taken to ensure its accuracy?To ensure its accuracy, parallax error should be reduced. The load has to locate at the point under the axis that we looking for. When obtaining results, make sure the hanger and masses is not swinging and statically remain at same point. Besides, before experiment, input 1 and input 2 should set to zero to increase accuracy.

7.0 CONCLUSIONAfter the experiment, we have obtained all the result and done all the calculation. The objective is achieved as fix moment value for fixed and propped cantilever beam collected during experiment. However, to get a more accurate result, we must reduce the parallax error and human error during experiment. Before record the result, we must make sure the hanger with load is not swinging and stable. We also have to make sure the load is perpendicular to the distance set during experiment. This experiment is important in determining the suitability of design to support load and durability of structure.

8.0 REFERENCES/APPENDIX1. B.D. Nautiyal, Introduction to Structural Analysis2. Dr. B. C. Punmia, Ashok Kumar Jain, Arun Kumar Jain, Mechanics of MaterialRecording for result during experiment

Adjusting input to set zero

Loosing the screw to do experiment for propped cantilever beam