Bending: Second Moment of Area and Solid Edge

MEM23061A Test Mechanical Engineering Materials Lab. BEAM BENDING The bending of beams is one of the roughly important types of strain in engineering. Bendingis more likely to be a critical stress thanother types of stress like tension, compression etcetera In this laboratory, we will be determining the Modulus of Elasticity E (also c solelyed Youngs Modulus) of the various materials and using Solid Edge to determine the Second Moment of Area for the opposite cross-sections. pic Equations Use units Force (N), Length (mm), Stress (MPa) E = Youngs Modulus or Mod of Elasticity (MPa)I = 2nd Moment of Area or Area Moment (mm4). lowlife calculate using SolidEdge sketch. BENDING pic In our case, we must first convert the mass to Newtons (N). W = kg * 9. 81 L is the span length in (mm). I is the Second Moment of Area in (mm4). We can calculate this for a rectangle using a simple formula pic For other shapes it is not so simple. We need to calculate these using a program such as Solid E dge (see below). Determining the value of E in MPa. From the above equation, excursus z = W * L3 / (48 * E * I) so E = W * L3 / (48 * z * I) Determining Stress in MPa.From the above equation, Bending Moment (Nmm) M = W*L / 4 and MaximumStress (MPa) f = M * y / I where y = distance from centroid to the bottom (or top) of the beam. This is simply half the depth for all the symmetrical beams except the channel. To find the centroid for the channel you need to use Solid Edge again (same as the Ixx window) pic Laboratory 1. Load another beam onto the rig. 2. place dial gauge to ensure it is touching the beam. Zero the dial face by rotating the lense and locking in place. 3. Apply each load and disgrace the refraction measurement. . Check you have all recordings Beam material, beam cross-sectional dimensions, span length, deflection readings, masses. 5. Make estimates of the errors associated with each measurement. E. g. Parallax error, mis-alignment, mechanical play,incorrect defl ections etc 5. Repeat for adjacent beam pic Report 1. Use Solid Edge to calculate Ixx for each beam. Also determine the weight on CAD. Draw up the cross-section (either in part mode or as a draft). While you are still in the profile sketch (i. e. before going to a solid) go to top menuInspect Area gt Click Area Information button in Ribbonbar (click inside the area you want to inspect) Click on the greenness arrow in Ribbonbar. You should see a table like this pic Ixx is the Second Moment of Area in bending witha vertical load. 2. Write a short report on the beam bending results. Each beam must have at least 3 weights. Make sure the deflection does not exceed the travel of the dial indicator (if so, use a lighter weight). 3. employ the equations above, calculate the value of E. Compare these values to the values obtained fromthe internet.E. g. Matweb. instal the working for 1 example calculation, but only give the rest of the answers in a table. Use Excel to do your calculati ons. 4. Determine the maximum stress for each mass (load) added to the beams. 5. Discuss any sources of error in the experiment esp measurements and how they might affect the results. Specify an overall error for your calculation of E. pic pic Using the dial gauge to measure deflection in the beam while under a load of 500g. pic pic The face of the dial gauge can be rotated to zero the scale.