SIMPLY SUPPORTED BEAM LABORATORY
OBJECT To investigate the relationship between the loading and deflection of several spans and different loading systems of a simply supported beam.
APPARATUS Beam rig, mild steel/aluminium/copper & brass beams, knife-edges, masses, weight hanger, deflection gauge and rule.
METHOD 1. Set up the mild steel beam so that it is sat on knife-edges with a span of 900mm and the dial gauge is in the centre.
2. Set the deflection gauge to zero.
3. Weigh the weight hanger and bracket, and then add them to the centre of the beam. Add 0.5kg and record the deflection.
4. Repeat with further 0.5kg masses, up to 4.5kg, recording deflections.
5. Check repeatability by taking off the individual masses and recording the falling deflections.
6. Set a span of 600mm, select a beam and set-up the deflection gauge to read zero deflection at the centre of the span. Place mass hangers at both ends of the beam to create four-point loading.
7. Apply loads in increments of 0.5kg upto 3kg and record the deflection.
8. Repeat the previous stage for the other beam materials.
SAFETY & Ensure masses are properly attached and do not slide off the hanger.
PRECAUTIONS
THEORY Hooke’s Law states that the deflection of an elastic material is directly proportional to the load applied to it.
For a four-point loading system of a simply supported beam it can be shown that the central portion of the beam is considered as an arc. The radius, R which is large compared with the chord length, L, is related to the deflection δ using the following expression:
A value of Young’s modulus of elasticity, E, can be determined.
RESULTS 1. Plot a graph of load against deflection for both the three-point and four-point loading systems for EACH beam.
2. Find the gradients of the slopes to determine the stiffness values of the beam set-ups.
3. For the three-point loading system draw the shear force and bending moment diagram for maximum bending moment created during the experiment.
4. Calculate the theoretical maximum deflection of the three-point loaded beam using the formula:
Where: W = Applied load (N)
l = Length of span (m)
b = Breadth of beam (m)
d = Depth of beam (m) E = Young’s modulus of elasticity (N/m2)
Notes: Load must be in Newtons, so kg must be converted to N.
For the shear force, bending moment diagrams and deflection calculation use the largest span and maximum load.
For the four-point loading system calculate the radius of curvature of each beam and estimate the E value from this value.
DISCUSSION Comment on the shape of the graphs – do the plots obey Hooke’s law? Do the lines pass through the origin of the graph? What is the relationship between the change in span and deflection for a constant load? Is the repeatability acceptable? How does the experimental deflection compare to the calculation? Are E values sensible? Review sources of error and suggest improvements.
CONCLUSION Comment on the practical findings of the experiment.
H – SINGLE PLANE BALANCING
OBJECT To resolve a rotating system that is unbalanced both statically and dynamically.
APPARATUS Norwood dynamic balancing rig (NDBR), weighing scales, masses, fixtures, rule.
METHOD 1. Position 600 g of mass at a radius of 127 mm at 20° on Disc A. Another mass totalling 1 kg should be placed at 76 mm at 80° on Disc A.
2. Construct a vector diagram (see fig.2) on A3 or A4 paper to the largest scale possible to determine the magnitude and angle of the ��closing’ vector.
3. Measure the angle of the resolving vector and determine the mass required to put the system in balance on a radius of 103 mm.
4. Make up the system using your resolved mass and angle.
5. Ask a member of staff to operate the NDBR rig to show that the system is now in balance.
6. Remove all masses.
7. Now place on Disc A: a mass of 200 g at a radius of 127 mm at 40°, a 500 g mass at a radius of 76 mm at 110° and 700 g mass at a radius of 127 mm at 100°.
8. Repeat stages 2 – 6 for the second system.
SAFETY The NDBR must NOT be operated without the direct supervision of a lecturer or laboratory technician.
PRECAUTIONS Ensure that masses are tightly fixed to the rig and that the spindles do not foul the frame when in rotation.
THEORY For a single plane rotating system to be in balance, the sum of the algebraic centripetal forces is zero. Since the angular velocity is the same it becomes dependent on the forces based on the mass multiplied by the radius of each component.
Fig. 2 Example vector diagram
RESULTS Show hand drawn vector diagrams. Remember to include the scale. Check your vector diagrams using either analytical methods or software.
DISCUSSION Comment on why balancing is so important when dealing with rotating systems. Consider why some systems become unbalanced. Give examples.
CONCLUSION Review sources of error and summarise the success of the experiment.
H � SINGLE PLANE BALANCING(550word)
SIMPLY SUPPORTED BEAM LABORATORY 550 word)
the Discussion for etch one should be 450
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