Question

An existing steel beam is in use in a building. Using a rectangular strain gauge rosette, the actual strains at point A have been recorded while being subjected to test loads which simulate crowd loading. It is necessary to calculate the principal stresses to check whether the beam is safe for its current purpose (ie: assess whether the stresses determined are less than the maximum permissible stresses)

 Figure 4: Strain gauge rosette location and recorded strains 

In this case it is reasonable to assume that the stresses along the z axis are 0 MPa 

For the steel used in the beam assume: 

E  =200 GPa 

u = 0.3 

Yield stress = 250 MPa 

Ultimate tensile stress = 400 MPa 

a) Using the strains recorded by the rosette, calculate the normal strains in the z and y axis direction and the shear strain in the z-y plane at point "A" 

b) Using Mohr's circle of strain (Mohr's circle must be shown and used) determine the magnitude of the principal strains at point "A". 

c) Calculate the principal normal stresses 

d) Calculate the maximum shear stresses in the z-y plane of the steel beam at point "A" 

e) Calculate the absolute maximum shear stress at point "A" 

f) If the maximum normal stress induced by an actual "crowd load" is not permitted to be greater than 150 MPa, and the maximum shear stress is not permitted to be greater than 90 MPa, can the beam be considered safe under crowd loading (as simulated by the test loads)? 

Answer 1