Problem 1
A steel beam with yield strength, ?yield = 300 MN/m2
is under a stress state as
follows:
?x = 30 MN/m2
, ?y = 150 MN/m2
, ?xy = 45 MN/m2
Using the Mohr’s circle method, determine the following:
a) The principal normal stresses and the maximum shear stress
b) Sketch a diagram the orientation of the planes of the principal normal
stresses and maximum shear stress relative to the original stress ?x and
?y
The normal and shear stresses on a plane 30° counterclockwise from the
horizontal plane where the 150 MN/m2 stress is acting. Under this stress
state, what is the safety factors using the Tresca failure theory, the
Rankine failure theory and the Von Mises Theory?
Problem 2
A steel bar of circular section 160 mm in diameter is to be used as a column with
both of its end pin jointed.
a) If the stress limit is 240 MN/m2 and the modulus of elasticity of steel is
2x1011 N/m2
, calculate the safe load if the length of the column is 8 m
with a safety factor of 1.75?