Question

(i)A steel cable, in a crane, is used to lift a mass 55000 kg, if the

        maximum upward acceleration of the load is 1.5 m/s² , calculate the

        minimum radius required in millimeters of the cable.

        Assume a safety factor of 7.0

(ii)A steel cable is under tension from a load it is supporting, what

         Condition must be fulfilled for it to break? [

         (iii) Why are steel rebars used in concrete structures?

 

  (iv)List three different types of stresses that can a cause material to break.

Answer 1

(i) The maximum tension:

$$T_\text{max}=kF=km(g+a).$$

The maximum strain:

$$\sigma_\text{max}=\frac{T_\text{max}}{A}=\frac{T_\text{max}}{\pi r^2},\\\space\\ r=\sqrt{\frac{T_\text{max}}{\sigma_\text{max}}}=\sqrt{\frac{km(g+a)}{\sigma_\text{max}}},\\\space\\ r=\sqrt{\frac{4350500}{\sigma_\text{max}}}.$$

Substitute the value of $\sigma_\text{max}$ to get the answer.

(ii) The applied stress must be greater than the maximum allowable value.

(iii) Because they hardly extend upon external loads

(iv) Tensile, compressive, shear.