Static determinate structures are those structures in which we compute axial forces by the application of static equilibrium alone. For plane frame, three such equations are:
For a statically determinate:
- Plane frame, m = 2j - 3
- Space frame, m = 3j - 6
Where m is the number of members and j is the number of joints.
Assumption is a plane truss
- The individual members are straight.
- The individual members are connected by frictionless hinges.
- The loads and reactions act only at the joints.
- The longitudinal axes of all members lie in one plane called middle plane of truss.
- The members are subjected to axial forces only B.M. and S.F. are neglected.
Method of analysis
The different method of analysis of static determinate structure are :
- Method of joints
- Method of sections
- Tension coefficient method
- Graphical method
Method of joints
This method is suitable only when two unknown forces meeting at a joint. We resolve all forces in two directions and apply the equilibrium equations to find the unknown forces.
Method of sections
This method is more useful when we have to compute the stresses in a limited number of members.
Merits of method of sections
- In a very large truss with more spans and you have to compute the force of any internal member.
- Usefull when number of unknowns are even three.
- Trusses like fink or french truss and scissor trusses.
Hints to determine the member of a truss that do not carry force
- A single force can not form a system in equilibrium.
- If two forces act at a joint, then for the equilibrium of the joint these two forces should act along the same straight line. The forces will be equal and opposite, but if the two forces are not along the same straight line. They must be zero.
- If three forces act at a joint and if two of them are along the same straight line then for the equilibrium of the joint, the third force should be zero.
