Lab 3 Report

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Northeastern University *

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2355

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Mechanical Engineering

Date

Jan 9, 2024

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pdf

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7

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ME 2356 Laboratory Template 1 Department of Mechanical and Industrial Engineering ME 2356: Laboratory for Mechanics of Materials Bending Test Submitted by Sydney Rodriguez Date Submitted: 11/30/23 Date Performed: 11/9/23 Lab Section: 12 Lab TA: Lindsey Young Course Instructor: Marguerite Matherne
ME 2356 Laboratory Template 2 1. Introduction This experiment explores how beams bend under various loads and introduces column buckling due to compression. It covers three-point bending, comparing calculated and measured deflections, and examines how extra supports affect beam deflection. The critical buckling load for columns under different support conditions is also studied. The aim is to understand beam behavior and the abrupt loss of stability in columns under compression. 2. Methods and results 2.1 Instron Procedure A material sample, with measured width and thickness and a set length of 110mm, was tested using an Instron machine. The upper jaw was lowered until it lightly touched the sample, set on two support bars. Bluehill software was utilized to set up a compression method with metric units, a test rate of 10 mm/min, and the selection of raw data for measurement. The test was initiated, monitoring the curve until it departed from linearity (usually after 10-15mm of deflection) and then stopped. Following the test, the specimen was removed from the machine and placed on a flat surface to observe any plastic deformation. Shear force diagram and Bending moment diagram including the maximum value of the bending moment (M max ) in terms of P and L.
ME 2356 Laboratory Template 3 Results Sample material and measurements table Table 1. Steel data. Parameter Initial value (mm) Length 200 Thickness 9.49 Width 25.41 Second moment of area, I 1.8098e03 (mm^4) Load vs. deflection plot for the predicted and experimental data Yield strength The yield strength, σy, at the given triangle is about 2092.57 N/mm. The location where the beam starts to yield The point at which yielding appears first is (3.3738, 6960.6) (where the line starts to curve).
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ME 2356 Laboratory Template 4 Discussion Answer any question from instruction under section “Instron: results, analysis, and reporting” (#6 and 7) The calculated values of the Youngs Modulus range from 170000 to 200000 MPa. This is close to the predicted values ranging from 190000 to 230000 found online. The results are extremely close and may be a bit off due to human error. If others were to repeat this experiment, they should expect similar results.
ME 2356 Laboratory Template 5 2.2 Beam deflection Procedure In the outlined experimental procedure, steel beams with specified dimensions—20mm in width and 3.25mm in thickness—were subjected to deflection and load distribution tests. The experiment began with the calibration of the measuring instruments. Load cells and dial gauges were set to zero to negate any initial readings that could skew the results. The beams were then placed on supports, the positions of which were determined as per the accompanying diagram. A weight hanger, applying a force of 2.5 N, was positioned at the designated point on the beam to simulate a point load. Subsequent measurements of the beam's deflection were taken at points C and D using the dial gauges, which are designed to measure small displacements with high precision. Concurrently, load cells recorded the reaction forces at the beam's supports. This was repeated for a beam that is indeterminate and determinant. Results Deflection and support forces (and moments where available) Table 2. Beam deflection data. Discussion Answer any question from instruction under section “Beam deflection: results, analysis, and reporting” (#3 and #4) o The beam with the larger deflection is the simply supported or determinate one. This is due to an extra acting moment. o The calculated and experiment values are far off but this is most likely due to the beam being slightly different or calculation errors. If someone repeated this experiment, they would achieve closer results toward the calculated values. Point Problem 1: simple support end Problem 2: overhang end Experiment value Calculate value Experiment value Calculate value Force @ A -1.08 1.40625 -1.53 -2.109 Moment @ A N/A N/A N/A 0.00574 Force @ B 3.75 3.90625 4.03 4.609 Deflection @ C -6.50 0.00053 -6.72 -0.0126 Deflection @ D 1.39 8.22 0.99 0.05589
ME 2356 Laboratory Template 6 2.3 Buckling Procedure The experiment was designed to observe the effects of compressive forces on steel beams with predefined dimensions of 600mm in length, 20mm in width, and 4mm in thickness. The procedure was initiated by setting all instruments measuring load to zero to ensure accuracy. Following this, a crank mechanism was employed to exert a compressive load upon the beam. The crank was turned to the right gradually until a noticeable deformation in the beam's shape was observed, or until the force readings stabilized or altered minimally, indicating the load limit of the beam. This was repeated for a pin-pin supported beam and a pin-clamp supported beam. Results Prediction of critical buckling forces from equations. Be sure to show the values of effective length factor that you use. Table 1. Beam deflection experimental data. pin-pin support pin-clamp support Experiment value Calculate value Experiment value Calculate value Experimental critical force 511 350.92 1076 501.31 Discussion Answer any question from instruction under section “Buckling: results, analysis, and reporting” (#3, 4, 5) o If both ends had fixed supports, the beam’s critical force would increase. o Some error could be due to the setup of the experiment and the use of a hypothetical Youngs Modulus value. If others repeated this experiment, they would hopefully get closer values to the calculated one.
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ME 2356 Laboratory Template 7 Appendix: MATLAB code % Isotron sample %clear data clearvars; clc; %read file filename = 'lab3test.csv' ; T = readmatrix(filename); %conversions time = T(:,2); displacement = T(:,3); force = T(:,4)*1000; %sample properties (mm) b = 25.41; h = 9.49; L = 200; % calculations I = (b * (h^3))/12; M = force*L/I; yield = M/I; % Young's Modulus (E) E = (force./displacement).*(L^3/(48*I)); E1= 190000; % Predicted values predicted = force.* L^3 ./ (48 .* I .* E1); bending = force./displacement; %plot load vs deflection figure(1) plot(displacement, force); hold on plot(predicted, force); hold on title( 'Load vs Deflection' ); xlabel( 'Deflection (mm)' ); ylabel( 'Force (N)' );