Mechanics question on vector statics

ashishsinghal

Determine the reactions at B and D when b = 60mm ?
(Diagram is attached)

Since B and D are hinged we don't know the direction as well as magnitude of the reaction forces at B and D. Hence we have 4 unknowns (Bx, By, Dx, Dy).

But I can't find 4 independent equations. I got three by ƩFx= 0, ƩFy= 0 and moment about B = 0. Where is the 4th equation. Please help.

Attached Thumbnails

 

tiny-tim

hi ashishsinghal!

it's static, so what can you say about the forces at C ?

Rap

Call the ABC piece number 1 and the CD piece number 2. You know the force at point A so you have six unknowns, the two components of force at points B, C and D. You have six equations:[tex]\sum F_{1x}=0[/tex][tex]\sum F_{1y}=0[/tex][tex]\sum F_{2x}=0[/tex][tex]\sum F_{2y}=0[/tex][tex]\sum \tau_1=0[/tex][tex]\sum \tau_2=0[/tex] where [itex]\tau[/itex] is torque. (I assume "b" is not an unknown).

ashishsinghal

Thanks Rap I got the answer.