Help understanding statically determinate/indeterminate structures

[steve321]

hi!

i have a bunch of questions where I'm suppose to indicate if a structure is statically determinate

i have way to do this that usually gives me a decent answer. i go with r > 3n means it's indeterminate, and r = 3n means it's determinate. r represents reaction forces, and n represents the # of parts in the structure member.

just by memory i have an idea of how many 'reaction forces' there are. if there's a pin (the little triangle), i stick in two forces. if it's a roller (the little wheel thingy) i pop in one, and if the bar appears to be fixed to a wall i stick in three forces. if there's a hinge you draw four arrows but only count two of them. (or at least this is what the book seems to do)

then, the number of 'bars' in the drawing represents the number of structures, although if the structure has a bunch of connecting horizontal members you seem to split those into two for some reason.

anyway as you can see i have all these little shortcuts that help me get the right answer, but i don't know what exactly I'm doing.

first, what exactly is a determinate structure? i know it's something that doesn't have any more supports than it needs, and has few reaction forces (enough to solve).. but what does this mean? how does this translate into any practical application? is a determinate structure stiffer? more stable? easier to _____? i don't understand why i need to know this magical, intangible property of a structure.

second, i don't really understand the connection types. the pin and the fixed bar both seem to be the same thing from what i can tell, and i have absolutely no idea what the 'roller' represents in real life, nor do i understand what the triangle on the little circles represents. likewise i don't understand 'internal hinge' from 'pinned truss node', those both look the same.

if anyone could point me in the direction of an article that explains this clearly, or summarizes what exactly I'm doing, that would be a huge help. i hate doing things without understanding them.

 

[PhanthomJay]

hi!

i have a bunch of questions where I'm suppose to indicate if a structure is statically determinate

i have way to do this that usually gives me a decent answer. i go with r > 3n means it's indeterminate, and r = 3n means it's determinate. r represents reaction forces, and n represents the # of parts in the structure member.

Although there are handy dandy formulas for indeterminacy in trusses, I'd stay away from them unless you were sure of the correct formula for determining same.

just by memory i have an idea of how many 'reaction forces' there are. if there's a pin (the little triangle), i stick in two forces.

Yes, in 2D , a vertical force and a horizontal force

if it's a roller (the little wheel thingy) i pop in one,

yes, perendicular to the roller support

and if the bar appears to be fixed to a wall i stick in three forces.

that should be 2 forces and a moment (couple)

if there's a hinge you draw four arrows but only count two of them. (or at least this is what the book seems to do)

hinge and pin can be treated as the same

then, the number of 'bars' in the drawing represents the number of structures, although if the structure has a bunch of connecting horizontal members you seem to split those into two for some reason.

I think your talking members in trusses..you can look up the rules for determinancy at the risk of confusuion

anyway as you can see i have all these little shortcuts that help me get the right answer, but i don't know what exactly I'm doing.

first, what exactly is a determinate structure? i know it's something that doesn't have any more supports than it needs, and has few reaction forces (enough to solve).. but what does this mean?

A determinate structure is one in which the forces and moments in the members can be solved by using the standard 3 equilibrium equations (sum of forces in x direction, sum of forces in y direction, and sum of moments about any point all equal 0.

.. how does this translate into any practical application? is a determinate structure stiffer? more stable? easier to _____? i don't understand why i need to know this magical, intangible property of a structure.

it is not magical...by adding supports or members, you do make the structure stronger and stiffer by reducing stresses and deflections, but often at a cost. A member that is fixed at both ends can take more load than a member that is pinned at both ends, but the costs of 'fixing' the end connections (by welding or plating and bolting the connection , for example) may negate the savings, or be impractical.
Also, the use of indeterminate structures (multiple reaction points) may not be good when designing for extremely low deflection tolerances.

second, i don't really understand the connection types. the pin and the fixed bar both seem to be the same thing from what i can tell,

no, the pin can handle 2 perpendicular forces (cannot translate but is free to rotate and thus incapable of supporting a moment), the fixed support can handle 2 forces and a moment (couple), unable to translate or rotate in the ideal case

and i have absolutely no idea what the 'roller' represents in real life,

free to rotate and free to translate in the sliding direction

nor do i understand what the triangle on the little circles represents

. this is a roller support, it can't move in one direction but it can move (slide or roll) in the other direction , as a skateboard does...you might want to consider the roller support as a skateboard attached to the member

likewise i don't understand 'internal hinge' from 'pinned truss node', those both look the same.

yes, they do...

if anyone could point me in the direction of an article that explains this clearly, or summarizes what exactly I'm doing, that would be a huge help. i hate doing things without understanding them.

google??

 

[steve321]

thank you! this is a huge help!

 

[steve321]

oh, and can you give me a real life example of the roller, and the pin on the roller? i can't think of any structures that sit on ball bearings or skateboards.

 

[rwisz]

Hello there,

Understanding statically determinate and indeterminate structures is important in structural engineering as it helps determine the stability and strength of a structure. A structure is considered statically determinate if all its supports and reactions can be determined using the equations of static equilibrium. This means that the structure has just enough supports and reactions to keep it in equilibrium. On the other hand, a structure is considered statically indeterminate if it has more supports and reactions than what is required to keep it in equilibrium. This means that the structure has redundant supports and reactions, making it more complex and difficult to analyze.

Knowing whether a structure is statically determinate or indeterminate is crucial in designing and analyzing structures. A determinate structure is easier to analyze and design because the equations of static equilibrium can be used to solve for all the unknown forces and reactions. On the other hand, an indeterminate structure requires more complex methods, such as the use of compatibility equations, to solve for the unknown forces and reactions.

The different connection types, such as pins, rollers, and hinges, have specific roles in a structure. A pin connection allows for rotation but not translation, while a roller connection allows for translation but not rotation. A fixed connection, also known as a moment connection, allows for both rotation and translation. These connection types are used in different parts of a structure depending on the required movement and load distribution.

I would suggest researching online for articles or resources that explain statically determinate and indeterminate structures in more detail. It may also be helpful to consult a structural engineering textbook for a deeper understanding. I hope this helps clarify some of your questions.