16232 Structural Mechanics Lab Study Four-Point Bending Test Aim: Evaluate the Young's modulus of stainless steel by a four-point bending test. Description: A uniform steel beam with rectangular cross-sectional area

(Fig 2) is simply supported at B and C (Fig. 1) under the conditions of AB=CD and BF=CF. During the experiment, the same amount of load is applied at A and D simultaneously and the corresponding deflection at the middle of the bar, F, is tracked by a deflection gauge. The tensile strain associated with the deflection is directly measured by a typical resistance strain gauge (Fig 4). By increasing the load at A and D, a series of data on load-deflection and load-tensile strain at F can be obtained. With these data available, Young's modulus of the steel can be calculated using simple bending theory. W m B A Deflection gauge B n R h F n Fig.1 Front view of experimental setup A R m C O Fig. 3 Schematic illustration of curvature of the beam under loading III W Neutral Axis b V Position of deflection gauge Fig. 2 Dimension of cross-sectional area of the beam t CON Strain gauge Fig. 4 Top view of beam section with deflection gauge and strain gauge 123ASONS 4 5 6 7 8 9 The Bending Relationship Μ σ W(kg) 5 (mm) loading || E IyR where M is the bending moment in the beam, I is the second moment of area about the neutral axis, ♂ is the direct stress at a point with distance y from neutral axis, E is the Young's modulus of the material, R is the radius of curvature of neutral axis. Experimental Procedure 1. Mounting the beam upon the supports at B and C and make sure that the beam is symmetrical with respect to the deflection gauge (Fig.1). 2. Make sure that the deflection gauge sits beside (not on the top of) the strain gauge (Fig. 4). 3. Measure m, n, b with ruler and the thickness of the beam, t, with caliper. 4. Load the beam at A and D with provided weights in an incremental fashion. 5. Note down the load w (in kg) and corresponding read-out from deflection & (in mm) and strain gauges ɛ, (3 readings in micro strain) in the table below. 6. Unload the beam at A and D with provided weights in an incremental fashion. 7. Note down the load w (in kg) and corresponding read-out from deflection d (in mm) and strain gauges ɛ, (3 readings in micro strain) in the table below. Data Spreadsheet* ε (µ)** loading 5 (mm) unloading ε (µ)** unloading ** The value obtained from the strain gauge has a unit of micron, µ. Thus the absolute strain value is the read-out multiplied by 10-6 The completed report will be submitted online in week 5 of Semester 2. See "Guide to Report Writing " and "Structural Lab Report Template" on Myplace