ANALYSIS OF STATICALLY INDETERMINATE

STRUCTURES

1. SMALLER STRESSES

ADVANTAGES

2. GREATER STIFFNESSES

ADVANTAGES

3. REDUNDANCIES

ADVANTAGES

3. REDUNDANCIES

ADVANTAGES

1. STRESSES DUE TO SUPPORT SETTLEMENTS

DISADVANTAGES

2. STRESSES DUE TO TEMPERATURE CHANGES AND FABRICATED ERRORS

DISADVANTAGES

FUNDAMENTAL RELATIONSHIPSANALYSIS OF INDETERMINATE STRUCTURES

Equilibrium equations Compatibility conditions Member force-deformation relations

METHOD OF ANALYSIS

FORCE (FLEXIBILITY) METHODS DISPLACEMENT (STIFFNESS) METHODS

FORCE METHOD

Small structures with few redundants Used to derive the member force-deformation

relations to develop the displacement method

DISPLACEMENT METHOD

More systematic Can be easily implemented on computers

METHOD OF CONSISTENT DEFORMATIONS- FORCE METHOD James C. Maxwell in 1864 Involves removing enough restraints from

the indeterminate structures to render it statically determinate.

Primary structure-determinate structure, which must be statically stable

Redundant restraints-excess restraints removed from the given indeterminate structure to convert it to the determinate primary structure.

PROCEDURE FOR ANALYSIS Determine the degree of indeterminacy

of the given structure. (n not greater than 1)

Select one of the support reactions as redundant.

Remove the restraint corresponding to the redundant from the given indeterminate structure to obtain the primary determinate structure.

PROCEDURE FOR ANALYSIS a. draw a diagram of the primary structure with only the

external loading applied to it. b. draw a diagram of the primary structure with only the unit

value of the redundant applied to it. Write the compatibility equation by setting the algebraic sum of

the deflection of the primary structure at the location of the redundant due to the external loading and the equal to the given displacement (or rotation) of the redundant support of the actual indeterminate structure. (the algebraic sum of deflections due to the external loading and the redundant can be simply set equal to zero).

Compute the deflection of the primary structure at the location of the redundant due to the external loading and due to the unit value of the redundant.

PROCEDURE FOR ANALYSIS Substitute the values of deflections (slopes)

computed in step 6 into the compatibility equation, and solve for the unknown redundant.

Determine the remaining support reactions of the indeterminate structure either by applying the three equilibrium equations to the free body of the indeterminate structure or by superposition of the reactions of the primary structure due to external loading and due to the redundant.

PROCEDURE FOR ANALYSIS Once the reactions have been evaluated, the

other response characteristics of the indeterminate structure can be determined. Either through equilibrium or by superposition of the responses of the primary structure due to external loading and due to the redundant.