Lab 4 - Deflections of Beams

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Centennial College *

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204

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Mechanical Engineering

Date

Jan 9, 2024

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4

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Page 1 of 4 MT-204 / ROBO-240 Lab FILL OUT THIS SECTION IN PEN Course Code and Section Name Student Number Attendance for Part A (dd/mm/yy) / / Lab Instructor’s signature Attendance for Part B (dd/mm/yy) / / Lab Instructor’s signature DEFLECTIONS OF BEAMS OBJECTIVE To experimentally determine the deflections of a simply-supported beam and to compare with theoretically calculated deflections. PART A EXPERIMENTAL DEFLECTION OF A SIMPLY-SUPPORTED BEAM 1- Using the TecQuipment SM 1004 Beam Apparatus, clamp two simple supports/load cells at positions of 500 mm and 1100 mm. 2- Insert the locking pins into the two simple supports/load cells, then check that both are “OFF”, thus providing rigid simple supports. 3- Place the 6.4 mm thickness steel beam on the supports to provide a simply-supported beam with a span of L = 600 mm between simple supports A and B , as shown. 4- Place an empty weight hanger at a distance a = 450 mm from support A. 5- Clamp a deflection indicator at position x = 50 mm from support A and turn “ON”. 6- Press “ORIGIN” to zero the deflection reading. 7- Add a total load of P = 40 N to the weight hanger then read, and record in the following table, the experimental downward (negative) deflection y exp . 8- Remove the load from the weight hanger then re-position the deflection indicator at the next value of x in the table. 9- Repeat Step 6 onwards until all the values of x in the table have been used.
P = 40 N L = 600 mm a = 450 mm b = 150 mm E = 210 GPa I = BH ³/12 = (19 mm)(6.4 mm)³/12 = x (mm) y exp (mm) y theo (mm) 50 100 150 200 250 Each Theoretical y (5 Points) 300 350 400 450 500 550
PART B ANALYSIS OF THE DEFLECTION OF A SIMPLY-SUPPORTED BEAM 1- Based on the appropriate case and formula(s) at the end of this lab sheet, with the given information about the modulus of elasticity E of steel and the calculated value of the moment of inertia I of the beam cross section (using the given cross section dimensions), calculate and record in the previous table, the theoretical downward (negative) deflection y theo , to the nearest 0.01 mm. 2- Using the following graph, plot the experimental data points as solid circles (●) and the theoretical data points as hollow circles(○); the deflection at each of the two supports is zero. (20 Points) 3- Draw a smooth curve through the data points using a solid line for the experimental deflection curve and a dashed line for the theoretical deflection curve, labelling the curves as “Experimental “ and “Theoretical”. (20 Points) Examining the deflection curves above, comment on the degree of agreement between the theoretical and experimental curves: (5 Points)
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