Two bars are joined together on their ends as shown in the figure below. The bars are then fixed on both ends and an axial force P is applied at the interface between the two bars. The length (L) and modulus elasticity (E) of the two bars are equal. The cross-section area of bar 1 is double than the bar 2. Compute the stresses in each bar. Assume that the bar is behaving as a one-dimensional bar element and each bar is one element. 2A, E 1 L 2 A, E 어 2 P 3 L X 1. Construct the stiffness matrix of elements 1 and 2. 2. Assemble the global stiffness matrix of this simple structure. 3. Assign the boundary conditions and reduce the linear system. 4. Solve the reduced system. 5. Compute the stresses of the two bars. 6. Compute the support reactions. 7. Verify (or check) the results using a force balance.
Plane Trusses
It is defined as, two or more elements like beams or any two or more force members, which when assembled together, behaves like a complete structure or as a single structure. They generally consist of two force member which means any component structure where the force is applied only at two points. The point of contact of joints of truss are known as nodes. They are generally made up of triangular patterns. Nodes are the points where all the external forces and the reactionary forces due to them act and shows whether the force is tensile or compressive. There are various characteristics of trusses and are characterized as Simple truss, planar truss or the Space Frame truss.
Equilibrium Equations
If a body is said to be at rest or moving with a uniform velocity, the body is in equilibrium condition. This means that all the forces are balanced in the body. It can be understood with the help of Newton's first law of motion which states that the resultant force on a system is null, where the system remains to be at rest or moves at uniform motion. It is when the rate of the forward reaction is equal to the rate of the backward reaction.
Force Systems
When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence the system is in balance or equilibrium. When two or more materials interact then more than one force act at a time, hence it is called as force systems.
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