Rigid bar is supported by two short white spruce wooden post and spring If each of the post have unloading length of 1m and cross section area of 600 ` mm^2` and spring stiffness of k=3MN/m and unscratched length of 1.02m. Determine the force on each wooden post after the load is applied.

 

Rigid bar is supported by two short white spruce wooden post and spring If each of the post have unloading length of 1m  and cross section area of 600 ` mm^2` and spring stiffness of k=3MN/m and unscratched length of  1.02m. Determine the force on each wooden post after the load is applied

 

Solution - 

Given,

Area ,A= 600 `mm^2` = 600 x `10^-6`  `m^2`

Also , we know that

 Elastic modulus of the white spruce wood , E=9.65 Gpa =9.65 x `10^9` Pa

 

Now,  From the figure

Taking moment about C,  `F_a` x 1 - `F_b` x 1 = 0

So,  `F_a` = `F_b`=F

Now,  forces in vertical direction

2F + `F_s` - 50x2x`10^3` = 0 ____________________(1)

Also, using compatibility equation

    `F_a` + 0.02 = `F_s`

 F x (AC) / Area x E + 0.02 = `F_s` / k

` \fracF{600times10^{-6}\times\9.65\times10^9}` + 0.02 = `F_s`/3x`10^6`

1.727 F + 2 x `10^5` = 3.33 _________________(2)

 

On solving equation (1) and (2) we get

F= 15611.8 N and  `F_s` = 68776.26 N

 

Hence , Force on each wooden post wil be 15611.8 N