Quiz 2 - Solution

1. Bar AB rotates clockwise by 1^o about point A.  Using the linear theory, determine

a) the displacement v of point B in inches.

b) the elongation d of cable BC in inches.

c) the rotation r of cable BC in radians.

a) v = 6(12)(1)(p/180) =  1.257 in

b) d = vcosq = 0.8v =  1.005 in

c) r = vsinq/5 = 0.6v/5(12) = 0.0126 rad.

2. Bars AB and AC elongate, respectively, by d₁ = 0.01 inch, and d₂ = - 0.02 inch.  Determine the displacements u and v of joint A using the linear theory.

d₁ = 0.5u - 0.866v = 0.01

d₂ = -0.707u - 0.707v = - 0.02

Solve.  From second equation,

v = - u + 0.02828

Into first equation

u(0.5 + 0.866) = 0.01 + 0.0245

u = 0.025  in.

v = 0.0030  in.