Correct Answer - Option 2 : 2.5
Concept:
Allowable stress (or Permissible stress): It is the maximum stress allowed at which a member is expected to perform its function without failing under the given loading conditions.
Working stress: It is actual stress at which the member is subjected to under the given loading conditions and should never cross allowable stress.
Factor of Safety (FOS): It represents the required margin of safety for a structure or component and often decided according to code, law, or design requirements. In general, FOS is given by,
\({\rm{FOS}} = \frac{{{\rm{Allowable\;Stress}}}}{{{\rm{Working\;Stress}}}}\)
Calculation:
\({\rm{Allowable\;stress}} = \frac{{{\rm{Maximum\;Load\;on\;the\;specimen}}}}{{{\rm{Cross\;sectional\;Area\;of\;the\;specimen}}}} = \frac{{125}}{{250}}\frac{{{\rm{kN}}}}{{{\rm{m}}{{\rm{m}}^2}}} = 0.5{\rm{\;}}\frac{{{\rm{kN}}}}{{{\rm{m}}{{\rm{m}}^2}}}{\rm{\;\;}}\)
\({\rm{Working\;stress}} = \frac{{{\rm{Working\;Load\;on\;the\;tie}}}}{{{\rm{Cross\;sectional\;Area\;of\;the\;tie}}}} = \frac{{80}}{{50\; \times \;8}}\frac{{{\rm{kN}}}}{{{\rm{m}}{{\rm{m}}^2}}} = 0.2{\rm{\;}}\frac{{{\rm{kN}}}}{{{\rm{m}}{{\rm{m}}^2}}}{\rm{\;\;}}\)
\(\therefore {\rm{\;FOS}} = \frac{{{\rm{Allowable\;Stress}}}}{{{\rm{Working\;Stress}}}} = \frac{{0.5}}{{0.2}} = 2.5\)