To determine the maximum allowable stress (fo) for the given truss assembly made of A992 steel, we must consider both the yield strength and the buckling strength of the members.
The yield strength (σy) of A992 steel is given as 50 ksi. This means that the maximum stress the material can withstand before yielding is 50 ksi.
For a circular cross-section, the buckling stress can be calculated using the formula:
fcr = π2 E / (K2 L2)
where:
E = modulus of elasticity = 29,000 ksi
K = effective length factor based on end conditions (assumed to be 1 for fixed ends)
L = length of the member.
However, since the maximum stress can be affected by both yield and buckling, we should use the lower of the two to ensure safety. In most cases for steel members under axial loads, the yield strength controls unless the member is long and slender.
Final Conclusion:
Given the parameters, the maximum allowable stress will generally be determined by the yield strength of the material, which is 50 ksi. Thus, the maximum fo for this assembly should be limited to this value to avoid yielding the steel.
In summary, the maximum allowable stress fo for the truss assembly is:
- fo = 50 ksi