a) Explain the concept of \"Free-Body Diagram\" as used for the analysis of engi

Question

a) Explain the concept of "Free-Body Diagram" as used for the analysis of engineering (20 points) mechanics problems. Mention the steps that are needed to estimate the "internal loads" ina mechanical system. b) A person weighing 135 kg sits on the edge of the picnic table as shown. The vertical pie supporting the table is made of Aluminum 6061-T4 with Sy 145 MPa. a) Considering the combined effect of the person's weight and its bending moment at section A-A, estimate the maximum normal stress in the pipe. 60 points) Load Tablecop Pipe 170 mm ii) Estimate the safety factor based on yield strength of the pipe material. (20 points)

Explanation / Answer

a) free body diagrams is a sketch of a object showing all the forces acting on the body. This helps in visualizing the entire forces acting on a object. The object graphically shows forces, moments and respective reactions.

Steps to calculate internal loads in a mechanical system is as follows

1) Calculation of Reactions at the support

2) Once the reactions are calculated, take any one point with known reactions and resolve the balance forces

3) Use vector geometry an sum of forces = 0 to solve other member forces

4) Repeat process untill all members are solved

b) Stress = Force / Area = 1350N/ (pi/4*170^2) = 0.06 N/mm2

Moment= Force*Perpendicular distance=1.35KN*1.1m=1.485KN-m

i) Normal Stress = M*(d/2) / (Pi/64*d^4)

=1.485*(0.17/2)/(0.05*(0.17^4-0.163^4)

=0.126225/(0.05*(0.000835-0.000706)) = 0.126225/0.0000645 =1957 N/mm2

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