Statically indeterminate or statically determinate

In summary, the conversation discusses a question about a statically determinate beam with 6 reactions. However, the author's equation of r=n+3 is incorrect and the beam is actually statically determinate with 4 reactions. When looking at the entire beam, only 4 reactions are considered, but when splitting the beam into two parts, the internal reactions at joint B must also be taken into account, making a total of 6 reactions. The wording and equations used in the question are confusing and there may be additional equations needed to solve the problem.
  • #1
chetzread
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1

Homework Statement


in this question , it's stated in the beginning that there are 6 reactions ... But , the author gave the equation r = n +3 , r = 4 , n = 1 ...It's statically determinate ...

Homework Equations

The Attempt at a Solution


IMO , the author's is wrong . his original 's intention is to show that the question is statically indetreminate where r > n+3 ( r = 6 , n =1 ) ...so, he broke up beam into 2 parts to solve this question?
 

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  • #2
You must be careful using these equations for determinancy. The 2 reactions at the joint B are internal to the system. R is the number of external reactions, which is 4, n is the number of internal joints or hinges.
 
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  • #3
PhanthomJay said:
You must be careful using these equations for determinancy. The 2 reactions at the joint B are internal to the system. R is the number of external reactions, which is 4, n is the number of internal joints or hinges.
Only 1 reaction at joint B which is internal to the system , right ? which is only HB ?
 
  • #4
PhanthomJay said:
You must be careful using these equations for determinancy. The 2 reactions at the joint B are internal to the system. R is the number of external reactions, which is 4, n is the number of internal joints or hinges.
Can you list out what is the reaction force ,the reaction force that i gt are : HA , VA , VB and VC ?
 
  • #5
What reactions are you talking about? External at the supports ? Or both internal and external. Also don't forget the moment reaction at A.
 
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  • #6
PhanthomJay said:
What reactions are you talking about? External at the supports ? Or both internal and external. Also don't forget the moment reaction at A.
The static determinate beam refer to the beam that has been separated (part AB ) , If so , the reaction (r) in r = n+3 refer to Moment at A , HA , VA and VB ?

If I didnt get the beam separated , i would have 6 reactions , which are Moment at A , HA , VA, VB , HB , and VC ? this is statically indeterminate beam , where r = 6 > (n+3) , where n=1 , and n+3 = 4 ?
Since this is this is statically indeterminate beam , so we can't solve the problem ? So , we need to break up the beam into 2 different sections , so that we can solve the forces ?

Is my idea correct ?
 
  • #7
chetzread said:
The static determinate beam refer to the beam that has been separated (part AB ) , If so , the reaction (r) in r = n+3 refer to Moment at A , HA , VA and VB ?
the equation r = n+3 applies to the entire beam, not its parts. When you look at AB separately, you left out HB as a possible reaction.
If I didnt get the beam separated , i would have 6 reactions , which are Moment at A , HA , VA, VB , HB , and VC ?
no, you just have 4.
this is statically indeterminate beam , where r = 6 > (n+3) , where n=1 , and n+3 = 4 ?
The beam is statically determinate. You just have to look at each part.
Since this is this is statically indeterminate beam , so we can't solve the problem ? So , we need to break up the beam into 2 different sections , so that we can solve the forces ?

Is my idea correct ?
the beam is statically determinate. You do have to break it into parts to solve, but you only need the 3 equations of equilibrium to solve . Indeterminate beams require other equations involving deflections/compatability analyses.
 
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  • #8
PhanthomJay said:
the equation r = n+3 applies to the entire beam, not its parts. When you look at AB separately, you left out HB as a possible reaction.
no, you just have 4. The beam is statically determinate. You just have to look at each part. the beam is statically determinate. You do have to break it into parts to solve, but you only need the 3 equations of equilibrium to solve . Indeterminate beams require other equations involving deflections/compatability analyses.
I'm getting more confused now , can you state which are the 4 reactions ?
 
  • #9
PhanthomJay said:
the equation r = n+3 applies to the entire beam, not its parts. When you look at AB separately, you left out HB as a possible reaction.
no, you just have 4. The beam is statically determinate. You just have to look at each part. the beam is statically determinate. You do have to break it into parts to solve, but you only need the 3 equations of equilibrium to solve . Indeterminate beams require other equations involving deflections/compatability analyses.
It's stated in the beginning of the question ? there are 6 reactions exist in beam
 
  • #10
When you look at the entire 2 parts as one whole beam, there are 4 reactions, 3 at A and 1 at C. Those are the 4 that are used for the determinancy equation. When you split the beam into 2 parts, then the internal reactions at B come into play. Total of 6. The wording is not clear, The determinancy equations are also confusing, and there are others.
 
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  • #11
PhanthomJay said:
When you look at the entire 2 parts as one whole beam, there are 4 reactions, 3 at A and 1 at C. Those are the 4 that are used for the determinancy equation. When you split the beam into 2 parts, then the internal reactions at B come into play. Total of 6. The wording is not clear, The determinancy equations are also confusing, and there are others.
why when we look at the entire part , we don't have to consider thw 2 reactions at joint B ?
 
  • #12
chetzread said:
why when we look at the entire part , we don't have to consider thw 2 reactions at joint B ?
Because there is no external support at B. The supports are at A and C.
When you draw the free body diagram of the entire part, only applied forces and externall support reactions at A and C show in the diagram. Forces at B are internal and do not show. When you draw a ffree body diagram of each part, only then will the B forces show in the diagram.
 
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  • #13
PhanthomJay said:
Because there is no external support at B. The supports are at A and C.
When you draw the free body diagram of the entire part, only applied forces and externall support reactions at A and C show in the diagram. Forces at B are internal and do not show. When you draw a ffree body diagram of each part, only then will the B forces show in the diagram.
The hinge is the external support that we could see , right ?
 
  • #14
chetzread said:
The hinge is the external support that we could see , right ?
You can see them but they are not outside the beam . Imagine that the support at A is a wall that the beam is anchored into, and that the support at C is a wall that the beam is resting on. There is no wall at B, so there is no outside support at B,
 

FAQ: Statically indeterminate or statically determinate

1. What is the difference between statically indeterminate and statically determinate structures?

Statically indeterminate structures are those that cannot be analyzed using only the equations of static equilibrium, while statically determinate structures can be analyzed using these equations alone.

2. How do you determine if a structure is statically indeterminate or statically determinate?

A structure is considered statically indeterminate if it has more unknown forces or reactions than the number of equations of static equilibrium available to solve for them. Conversely, a structure is statically determinate if it has the same number of unknowns as equations.

3. What are some examples of statically indeterminate structures?

A cantilever beam with an overhang, a truss with redundant members, and a continuous beam with more than three supports are all examples of statically indeterminate structures. These structures require additional equations, such as compatibility equations or virtual work equations, to solve for all unknown forces and reactions.

4. How do you solve for unknown forces in a statically indeterminate structure?

To solve for unknown forces in a statically indeterminate structure, additional equations must be used. These can include compatibility equations, virtual work equations, or the method of consistent deformations. These methods allow for the determination of unknown forces based on the behavior and deformations of the structure.

5. Why is it important to determine if a structure is statically indeterminate or statically determinate?

Understanding if a structure is statically indeterminate or determinate is important for the safe and efficient design of structures. Statically indeterminate structures can experience unexpected shifts in forces and reactions, making them more susceptible to failure. Additionally, the determination of unknown forces in these structures is crucial for ensuring structural stability and proper load distribution.

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