Tuesday, July 30, 2013

Methods of structural analysis - broad classification

You might have read my earlier posts on the determinate and indeterminate structures. Determinate structures can be analysed easily with the conditions of the equilibrium but the indeterminate structure needs other methods of structural analysis. These methods are broadly classified into two categories:

(1) Force Methods/ flexibility methods/compatibility methods.
(2) Displacement Methods/stiffness methods/equilibrium methods.

In the force methods the forces are taken as the redundant and then writing the equations in terms of the forces for the displacements and then applying the compatibility equations on these equations, we can find out the various forces. There are numbers of methods which come under this category:
(1) Virtual work method/Unit load method
(2) column analogy method
(3) Elastic Center method
(4) Three moment theorem
(5) Castigliano's theorem of minimum strain energy
(6) Mohr-Maxwell Theorem
 In the displacement methods the equations are written for the forces and then the unknown displacements are found by applying the equilibrium conditions on these equations. These displacements are put back into the initial equations to find out the forces.  Various Displacement methods are listed below:
(1) Slope displacement method
(2) Moment Distribution Method
(3) Minimum potential energy method
There is a condition to chose among the two and the condition is if,
(a) Static indeterminacy(Ds) < Kinematic indeterminacy(Dk), then we should use the force methods
(b) Kinematic indeterminacy(Dk) > Static indeterminacy(Ds) , then we should use the displacement methods.
Some of these methods are dealt in details in my other posts. 
Thank you.

Monday, July 8, 2013

Elastic constants (E, G & K)

If you are studying the structural engineering then there are these three elastic constants which you have to use in various theories.
(1)Young's modulus of elasticity E
(2) Modulus of rigidity G
(3) Bulk modules  K
E is the elastic constant which is defined as the linear stress over linear strain.
G is defined as the shear stress over shear strain.
K Bulk modulus is defined as the stress over volumetric strain.
Poison's ratio is another constant which is defined as the lateral strain over linear strain.(n)
Numerically E= 3k(1-2n)
                 also E=2G(1+n)