Bending: Second Moment of Area and Solid Edge

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  • Topic: Second moment of area, Beam, Elasticity
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MEM23061A Test Mechanical Engineering Materials
Lab. BEAM BENDING
The bending of beams is one of the most important types of stress in engineering. Bending is more likely to be a critical stress than other types of stress - like tension, compression etc. In this laboratory, we will be determining the Modulus of Elasticity E (also called Young's Modulus) of the various materials and using Solid Edge to determine the Second Moment of Area for the different cross-sections.

[pic]

Equations 
Use units: Force (N), Length (mm), Stress (MPa) 
E = Young's Modulus or Mod of Elasticity (MPa)
I = 2nd Moment of Area or Area Moment (mm4). Can 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 Edge (see below).

Determining the value of E in MPa. From the above equation,

Deflection   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
Maximum Stress (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. Adjust 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 record the deflection measurement.
4. 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....
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