Chapter 2, Problem 2.2.1P

A 10-ft rigid bar AB is supported with a vertical translational spring at A and a pin at B. The bar is subjected to a linearly varying distributed load with maximum intensity q₀. Calculate the vertical deform at ion of the spring if the spring constant is 4 kips/in.

  

To determine

Vertical deformation of the spring in given loading condition.

Answer to Problem 2.2.1P

The required value of the vertical deformation is $6.944\times {10}^{-3}ft$

Explanation of Solution

Given information:

  

  $\begin{array}{l}\text{Length}\text{(l)}\text{=}\text{10}\text{ft}\\ \text{Spring}\text{constant}(k)=4kips/in\end{array}$

Formula used:

  $Deformation({\delta }_A)=\frac{A_y}{k}$

  $Moment(M)=F\times D$

Calculation:

Let us convert the spring constant from kips/in to kips/ft;

  $\begin{array}{l}\Rightarrow 4kips/in\\ \Rightarrow 4\times 12\\ \Rightarrow 48kips/ft\end{array}$

Let us calculate the moment;

  $\begin{array}{l}{\displaystyle \sum M_B}=0\\ \Rightarrow -A_y\times 10+\frac{1}{2}\times 10\times 2\times \frac{10}{3}=0\\ \Rightarrow A_y=3.33kips\end{array}$

Now the deformation is;

  $\begin{array}{l}{\delta }_A=\frac{A_y}{k}\\ \Rightarrow {\delta }_A=\frac{3.33}{10}\\ \Rightarrow {\delta }_A=0.0694ft\end{array}$

Total deformation along the bar;

  $\begin{array}{l}\Rightarrow \frac{{\delta }_A}{L}\\ \Rightarrow \frac{0.0694}{10}\\ \Rightarrow 6.944\times {10}^{-3}ft\end{array}$