Structural analysis of methods|Civil engineering| Finite element analysis| Stiffness method| computer analysis

The structural analysis predicts the performance of a given structure under external loads and self weight. These technique are utilizes on matrix methods to analysis structures.These techniques are applied as code in computers.These methods like stiffness, flexibility and finite element methods can be used to analyze beams,trusses,frames and grids as shown in Fig.1.

Fig.1. Two dimensional Frame can be analyszed using below shown methods.

Click below tabs to see step by step process of strutural analysis methods.

Steps involved in stiffness method

1. Assemble the stiffness equations for the problem defined.

2. Define the element stiffness matrices.

3. Align them with global stifnness using coordinate transformation.

4. Assemble the elemental stiffness into global stiffness matrix.

5. Define the load vector.

6. Apply prescribed displacements or displacement boundary conditions.

7. Solve equations for the unknown displacements.

8. Conduct post-processing as required.

9. Calculate internal element loads and stresses.

10. Determine support reactions.

Steps involved in flexibility method

1. Select the system coordinates (Force and displacement). The force co-ordinates are selected where the external forces are applied and the displacement coordinates are selected where the displacement measurements are required.

2. Find the number of redundant from the degree of static indeterminacy of the structure and select appropriate redundant.

3. Select the members such that the structure coordinates occur only at their ends.

4. Determine the equivalent joint loads. The equivalent member end actions will replace the loads not acting at the joint coordinates.

5. Determine the individual member flexibility F_mi and the general flexibility matrix F_m.

6. Determine the following matrices:
P_ml member actions, P_m in primary structure for joint load W=1
P_mr member actions, P_m in secondry structure for redundant force R=1
P_sl member actions, P_s in primary structure for joint load W=1
P_sr member actions, P_s in secondry structure for redundant force R=1

7.Determine matrices [F_rl] and [F_rr] from the relation of [F_rl]=[P_mr]^T[F_m][P_ml] and [F_rr]=[P_mr]^T[F_m][P_mr] respectively.

8. Determine the redundant _R from the relation {D_r}=[F_rl]{W}+[F_rr]{R}.Thus, the value of redundant, {R}=[F_rr]^-1{{D_r}-[F_rl]{W}}. In general the support displacement {D_r} becomes zero.As result, the value of {R}=-[F_rr]^-1[F_rl]{W}

9. Determine the member end actions {P_m} from the equation: {P_m}=[P_rl]{W}+[P_mr]{R}

10. Determine the support reactions {P_s} from the equation: {P_s}=[P_sl]{W}+[P_sr]{R}

11. Calculate displacements at the coordinates using the relation: {D}=[F]{P}

Steps involved finite element method

1. Select suitable field variables and the elements.

2. Discritise the continua.

3. Select interpolation functions.

4. Find the element properties.

5. Assemble element properties to get global properties.

6. Impose the boundary conditions.

7. Solve the system equations to get the nodal unknowns.

8. Make the additional calculations to get the required values.

Refrence

1. Maity, D. (2009). Computer analysis of framed structures (1st ed.). I.K International Publishing House Pvt Ltd.