Why is Only One Reaction Shown at the Pinned Support?

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SUMMARY

The discussion centers on the analysis of a pinned support at joint A in a structural system, where the modulus of elasticity is E = 20 kN/(mm²) and the cross-section varies among members. Participants clarify the reactions at the pinned support, emphasizing that while only a horizontal reaction was initially shown, a vertical reaction must also be considered. The correct approach involves calculating the horizontal force at A and taking moments about point D to deduce the vertical reaction, ultimately leading to the conclusion that the vertical reaction at A is 10 kN upwards.

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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]
 

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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?
 
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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.
 
  • #10
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 ?
 
  • #11
fonseh said:
moment about D = VA(2) -20(1) = 0
The equation must include moments due to all the forces, including those at B.
 
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  • #12
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 ?
 
  • #13
fonseh said:
moment about D = -20(1) +VA(2) -20(1)+20(2) = 0 , Thus VA = 0 ?
Right.
 
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