# Unsymmetrical Bending and Shear Centre - 1 MMAN 3400...

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1 MMAN 3400 Mechanics of solids 2 Unsymmetrical Bending and Shear Centre Lab report Jiapeng Yu z5013347 Submit on: 06/05/2016 IntroducKon: This report includes two parts: unsymmetrical bending and shear centre. Unsymmetrical bending experiment shows that how to find the moment of iner<a, by measuring and calcula<ng the deﬂec<on of unsymmetrical beam in different angles with varied pulling weight. Shear centre experiment measures the displacement of the beam in two places with varied eccentricity of the load. Excel is used for result analysis and ploCng, and Mohr’s Circle analysis is also included in calcula<on part. Part 1: Unsymmetrical Bending Aim: Find the second moments of area of the beam,by measuring and calcula<ng the deﬂec<on of the unsymmetrical beam. Theory: For the moment that is not applied about the principle axes, which will cause two components, U and V, as the figure1.1 shows below: U-V plane is principal centroidal Axes, and x-y plane is orthogonal axes. is the angle of twist. The formula for calculate U and V shows below: ҁ Appendix_1.1 ҂ x y V U θ θ U = FL 3 6 E ( 1 I x + 1 I y ) + cos(2 θ ) ( 1 I y 1 I x ) V = FL 3 6 E sin(2 θ )( 1 I x 1 I y )
2 According to the formula above, Moth’s Circle method can be applied (Appendix_1.1) Apparatus: Handwheel securing thumbscrews Chuck(top&boRom) Specimen Digital indicators Shear centre beam Datum pegs Extension piece Hanger and mass BoRom plate (Appendix_1.2) Procedure: 1:Set up the equipment. 2:Check and ensure the beam at correct posi<on, and <ght the screws. 3:Ensure the indicator have about 10-11 mm forward and 2-3 mm backward travel in this posi<on. 4:Main lab process: (1) Zero indicators. Add the load on the end of the cord (120g, 240, 360g,and 480g) and record the number shows on two indicators respec<vely. (2) Loose top and bot screws, and rotate the specimen clockwise 22.5 degree(1/8 circle). Add the load form 120g to 480g as above process, and record the data. (3) Rotate the specimen clockwise to 45 degree (another 1/8 circle). Doing the process (2) un<l the specimen rotates 180 degree.
3 Results and CalculaKons: 1: Table (1) of Readings on digital indicators: Measured length of beam: L = 470 mm 2: Calculate the deﬂec<on for U-V axis. According to the Formula: Reading measurements in mm 120g 240g 360g 480g Left Right Left Right Left Right Left Right 0 -0.49 -0.65 -1.47 -2.81 -2.6 -5.72 -3.13 -6.26 22.5 -0.41 -0.75 -0.91 -2.03 -1.45 -2.86 -2.22 -4.21 45 -0.71 -0.21 -1.6 -0.7 -1.81 -1.54 -2.54 -2.48 67.5 -1.07 -0.24 -2.42 -0.79 -3.28 -1.12 -4.09 -1.56 90 -1.73 -0.59 -2.73 -0.9 -4.31 -1.68 -6.25 -2.5 112.5 -1.9 -1.14 -3.8 -2.34