Chapter 11, Problem 11.2.1P

A rigid bar of length L is supported by a linear elastic rotational spring with rotational stiffness ß_Rat A.

Determine the critical load Pcr for the structure.

  

To determine

The critical load for the given structure.

Answer to Problem 11.2.1P

The required value of the critical load is $\frac{{\beta }_R}{L}.$

Explanation of Solution

Given information:

  

  $Rotationalstiffness={\beta }_R$

Formula used:

  $Moment\left(M\right)=F\times D$

Calculation:

Let us find the sum of moment about A.

  $\Rightarrow {\displaystyle \sum M_A}=0$ ;

  

  $\Rightarrow P\left(\theta L\right)-{\beta }_R\theta =0$ ;

Solve for $P_{cr}$ ;

  $\Rightarrow P_{cr}=\frac{{\beta }_R}{L}$