Why is Only One Reaction Shown at the Pinned Support?

[fonseh]

Homework Statement

The modulus of elasticity of each member is E = 20kN/(mm^2) and the cross section of each member is 1000(mm^2) , except member EB and EC is 40(mm^2) , determine :
a) The vertical displacement at joint C
b) The horizontal dispalcemnet at joint C

at A , it's a pinned support , so there must be 2 reactions , right ?

Homework Equations

The Attempt at a Solution

Why the author showed one reaction( horizontal reaction) only ? Is it wrong ? [/B]

 

[haruspex]

Why the author showed one reaction( horizontal reaction) only ? Is it wrong ?

Suppose there is a vertical reaction. What do the force and moment sums tell you?

 

[fonseh]

Suppose there is a vertical reaction. What do the force and moment sums tell you?

what do you mean ? Can you please explain further?

 

[haruspex]

what do you mean ? Can you please explain further?

You can determine the horizontal force at A easily. Take moments about D. What do you deduce about the vertical reaction at A?

 

[fonseh]

Suppose there is a vertical reaction. What do the force and moment sums tell you?

what do you mean ? Can you please explain further?

 

[fonseh]

Suppose there is a vertical reaction. What do the force and moment sums tell you?

what do you mean ? Can you please explain further?

 

[fonseh]

Suppose there is a vertical reaction. What do the force and moment sums tell you?

what do you mean ? Can you please explain further?

 

[fonseh]

You can determine the horizontal force at A easily. Take moments about D. What do you deduce about the vertical reaction at A?

The vertical reaction at A create clockwise moment about D

 

[haruspex]

The vertical reaction at A create clockwise moment about D

Yes, but write the equations. First, find the horizontal force at A. Then take moments about D to find the vertical force.

 

[fonseh]

Yes, but write the equations. First, find the horizontal force at A. Then take moments about D to find the vertical force.

HA = 20kN to the left . moment about D = VA(2) -20(1) = 0 , VA = 10kN(upwards) , is it correct ?

 

[haruspex]

moment about D = VA(2) -20(1) = 0

The equation must include moments due to all the forces, including those at B.

 

[fonseh]

The equation must include moments due to all the forces, including those at B.

moment about D = -20(1) +VA(2) -20(1)+20(2) = 0 , Thus VA = 0 ?

 

[haruspex]

moment about D = -20(1) +VA(2) -20(1)+20(2) = 0 , Thus VA = 0 ?

Right.