1. Problem 10.103 Rod AB is attached to a block 160 N
at A that can slide freely in
the vertical slot shown.
Neglecting the effect of friction
and the weights of the rods,
determine the value of q
corresponding to equilibrium.
160 N
200 mm A B q C
800 N
200 mm D
100 mm

2. Solving Problems on Your Own
Rod AB is attached to a block
at A that can slide freely in
the vertical slot shown.
Neglecting the effect of friction
and the weights of the rods,
determine the value of q
corresponding to equilibrium.
Problem
160 N
800 N
200 mm
100 mm A B C D q
1. Apply the principle of virtual work. If a system of connected
rigid bodies is in equilibrium, the total virtual work of the external
forces applied to the system is zero for any virtual displacement
of the system.
1a. Define a virtual displacement. By using a single variable,
define a virtual displacement of all the forces that do work.

3. Solving Problems on Your Own
Rod AB is attached to a block
at A that can slide freely in
the vertical slot shown.
Neglecting the effect of friction
and the weights of the rods,
determine the value of q
corresponding to equilibrium.
Problem
160 N
800 N
200 mm
100 mm A B C D q
1b. Express the total virtual work done by the forces and
couples during the virtual displacement.
dU = F . d r and dU = M dq
where dU is the virtual work, F is a force undergoing a virtual
displacement d r, and M is a couple undergoing a virtual
rotation dq.
1c. Set the virtual work to zero and solve for the variable.

4. yA = 400 sin q dyA = 400 cos q dq xD = 100 cos q dxD = _ 100 sin q dq
Problem Solution
160 N
800 N
200 mm
100 mm A B C D q
Define a virtual displacement.
160 N
800 N A B C D q
200 sin q yA xD
yA = 400 sin q
dyA = 400 cos q dq
xD = 100 cos q
dxD = _ 100 sin q dq

5. _ ( 160 )( 400 cos q d q ) _ (800)(_ 100 sinq dq) = 0A B C D q
200 sin q yA xD
Problem Solution
Express the total virtual
work done by the forces.
Set the virtual work to
zero and solve for the
variable.
Virtual work:
dU = _ ( 160 N ) d yA _ ( 800 N ) dxD = 0
_ ( 160 )( 400 cos q d q ) _ (800)(_ 100 sinq dq) = 0
= 0.8 ; tan q = q = 38.7o
sin q
cos q