question_answer 7)

Four identical hollow cylindrical columns of steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 cm and 60 cm respectively. Assume the load distribution to be uniform, calculate the compressional strain of each column. The Young's modulus of steel is \[{{\text{S}}_{\text{LA}}}\text{,}{{\text{S}}_{\text{SA}}}\text{ and }{{\text{S}}_{\text{SL}}}\]

Answer:

Load on each column, \[\theta \]      \[{{\text{S}}_{\text{SL}}}\text{+}{{\text{S}}_{\text{LA}}}\text{cos }\!\!\theta\!\!\text{  =}{{\text{S}}_{\text{SA}}}\]                                                                                                    Compression strain \[\text{cos }\!\!\theta\!\!\text{ =}\frac{{{\text{S}}_{\text{SA}}}\text{-}{{\text{S}}_{\text{SL}}}}{{{\text{S}}_{\text{LA}}}}\]= \[{{\text{S}}_{\text{SL}}}\text{}{{\text{S}}_{\text{SL}}}\text{,}\]