# Why is Only One Reaction Shown at the Pinned Support?

• fonseh
In summary, the conversation discussed the determination of vertical and horizontal displacements at joint C in a structure where the modulus of elasticity and cross section of each member were given. The conversation also touched on the calculation of reactions at joint A using force and moment sums. The discussion concluded with the correct equation for calculating the vertical reaction at A.
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 ?

## The Attempt at a Solution

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

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fonseh said:
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
haruspex said:
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 said:
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?

haruspex said:
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 said:
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 said:
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 said:
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

fonseh said:
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.

haruspex said:
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 ?

fonseh said:
moment about D = VA(2) -20(1) = 0
The equation must include moments due to all the forces, including those at B.

fonseh
haruspex said:
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 ?

fonseh said:
moment about D = -20(1) +VA(2) -20(1)+20(2) = 0 , Thus VA = 0 ?
Right.

fonseh

## 1. What is a pinned support in a reaction?

A pinned support is a type of structural support that allows for rotation but restricts translation. This means that the support can rotate around a pin or hinge, but cannot move horizontally or vertically.

## 2. How does a pinned support affect the reaction of a structure?

A pinned support can only provide a reaction force in the direction perpendicular to the pin or hinge. This means that the support can only resist forces that try to push or pull the structure away from the pin, but cannot resist forces that try to move the structure horizontally or vertically.

## 3. What are some examples of structures that use pinned supports?

Some examples of structures that use pinned supports include bridges, cranes, and truss systems. These structures often require the ability to rotate at certain points while still maintaining stability and support.

## 4. How are the reactions at pinned supports calculated?

The reactions at pinned supports can be calculated using the principles of statics. By analyzing the forces and moments acting on the structure, the reactions at the support can be determined. This calculation is important in designing and analyzing the stability and safety of a structure.

## 5. What happens if a pinned support is replaced with a fixed support?

If a pinned support is replaced with a fixed support, the reactions at that support will change. A fixed support restricts both translation and rotation, meaning it can resist forces in all directions. This can significantly affect the overall stability and strength of the structure.

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