The lever is attached to the shaft A using a key that has a width d and length of 21 mm If the shaft is fixed and a vertical force of 200 N is applied perpendicular to the handle, determine the dimension d if the allowable shear stress for the key is t = 34 MPa

 The lever is attached to the shaft A using a key that has a width d and length of 21 mm If the shaft is 

fixed and a vertical force of 200 N is applied perpendicular to the handle, determine the dimension "d" 

If the allowable shear stress for the key is τ = 34 MPa.

ANSWER :- 

Now, from the figure :-

Given ,   allowed shear stress ,τ  = 34Mpa

              length , L = 21 mm = 0.021 m

 

              

Now ,  Taking moment about A 

Fa (20) - F(500) = 0

Fa(20)  -  200(500) = 0

So,  Fa = 5000 N

also , allowed shear stress , τ =  Fa/area

                           34000000   =  5000/(d)(0.021)

                                          d =  0.007 m = 7mm

So, the value of  "d" is 7mm