Problem: Determine the maximum value of the average normal stress

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Normal stress is defined as σ = P/A, with the maximum normal stress calculated as σ = P/(b*h/cos(θ)). The correct values for normal stress are σAB = 97.7 MPa and σBC = -66.5 MPa. A user miscalculated the cross-sectional area, which should be A = b*h = 300 mm², and suggested using a free body diagram to accurately determine force components. The discussion emphasizes the importance of correctly interpreting the figure and applying Newton's laws for precise calculations.
zartiox
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Hi guys.

Please look at the uploaded picture.
Normal stress is difined as: σ= P/A. And the Maximum normal stress σ = P/ (b*h/cos(θ)) ??

The right answers should be σAB= 97,7 MPa and σBC = -66,5 MPa. But how do I calculate it?

What I have tried:
Force AB: 40* sin(60deg) = 34,641 kN = 34,641 * 10^3 N

σAB= 34,641 * 10^3 N/((45-20)*12)/sin(60deg)) = 100 MPa
 

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zartiox said:
Hi guys.

Please look at the uploaded picture.
Normal stress is difined as: σ= P/A. And the Maximum normal stress σ = P/ (b*h/cos(θ)) ??

The right answers should be σAB= 97,7 MPa and σBC = -66,5 MPa. But how do I calculate it?

What I have tried:
Force AB: 40* sin(60deg) = 34,641 kN = 34,641 * 10^3 N

σAB= 34,641 * 10^3 N/((45-20)*12)/sin(60deg)) = 100 MPa
I think you are misreading the figure regarding the cross sectional area of the link...its just b*h, where b is (45-20) = 25 mm, and h is 12 mm. Thus, A = 300 mm^2.
But beyond that, you are not calculating the force correctly. You might want to draw a free body diagram of the joint at B and use Newton's 1st law in the x direction (sum of forces in x direction = 0) and y directions (sum of forces in y direction = 0), to solve for the force components in each link. Then the member force can be found from the sq rt of the sum of the squares.
 
Thank you very much, that explanation helped me to could compute it :)
 

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