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MECHANICS - CASE STUDY

    Introduction


Shelf System

 

A new shelf system is planned to store large crates. The shelves are relatively short but carry a large distributed load. Each "T" beam is firmly fixed to the wall and acts as a cantilever beam. The design team would like to know what the largest shear stress in the "T" at the joint between the top flange and bottom web (point A).

What is known:

  • Each beam is loaded with a distributed load of 50 kN/m.
  • Location of point A is known for a given cross section, but it is not known along the length of the beam.
  • The dimensions of the beam are given in the diagram. All beams are the same dimensions.
   
  Question

 

What is the maximum shearing stress at point A anywhere along the beam length? What is the maximum normal stress?

   
  Approach

 
  • Determine the maximum bending moment and shear load using shear-moment diagrams.
  • Calculate the shear stress and bending stress for the location with the maximum moment and shear load.
  • Analyze the stress using a stress element.
  • Rotate the stress element so that the orientation gives a maximum shear.
  • Rotate the stress element a second time to give the maximum normal stress.
     
   
 
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