[Solved] The equation for degree of static indeterminacy = (m + t) - (2024)

FAQs

What is the equation for statically indeterminate? ›

The equation for degree of static indeterminacy = (m + t) - 3j is true for which of the following frames, where m is the number of unknown member forces, r is unknown reaction components and j is the number of joints?

Indeterminate truss

Both equilibrium and deformation must be included in the member load analysis. For this indeterminate truss, the compatibility equation for each member elongation is: e = FL/EA = uC cosθ + vC sinθ . Here E, A and L for each member will influence the member loads.

Statically Indeterminate Analysis

The force (flexibility) method - This method involves converting the indeterminate structure to a determinate structure by removing the additional unknown reaction forces and replacing them with a known reaction force equal to one unit force.

Concept: If the number of unknown reaction are more than the number of equilibrium equation available then structure is called indeterminate structure and degree of indeterminacy is given by static indeterminacy. Some important cases are: Pin jointed plane frame, Ds = m + r - 2j.

The degree of static indeterminacy (DSI) of a structure tells us which methods are suitable for analysing it. If a structure is statically determinate, i.e., DSI=0, then it suffices to use equilibrium to determine the section forces.

Essentially, a problem in statically indeterminate if there are more unknown variables then there are equations you can use to solve for the unknowns. This means it cannot be solved using equilibrium equations alone. You would need to simplify the problem or make as assumption for it to be solved.

If the equilibrium equations are not sufficient to analyse the structure for the unknown forces, the structure is said to be statically indeterminate. Page 5. 5 | Page.

In statics and structural mechanics, a structure is statically indeterminate when the equilibrium equations – force and moment equilibrium conditions – are insufficient for determining the internal forces and reactions on that structure.

A statically determinate structure is one that is stable and all unknown reactive forces can be determined from the equations of equilibrium alone. A statically indeterminate structure is one that is stable but contains more unknown forces than available equations of equilibrium.

If m + r < 2j then truss is unstable. If m+ r = 2j then truss is statically determinate and stability is checked by visual inspection. If m + r > 2j then truss is statically indeterminate and stability is checked by visual inspection.

What if truss is statically indeterminate? ›

However, a statically indeterminate truss structure is one in which the number of unknown forces and reactions exceed the number of equilibrium equations. It necessary to use compatibility equations to solve for the unknowns. Multiple load paths exist within a statically indeterminate truss structure.

4.3 Examples

We will obtain, as a practical application, the degree of static indeterminacy of some structures. This structure consists of 2 members and 3 joints. Joint C is free and joints A and B are supports, fixed and pinned, respectively. Therefore, the number of redundant forces is 2.

Statically Indeterminate Structure: Those structures where all the member forces and support reactions cannot be evaluated using equations of static equilibrium only and need additional compatibility equations are called statically indeterminate structures. e.g. fixed beam, continuous beam 2-hinged arch.

Simply supported beams

A simply supported beam is one that rests on two supports and is free to move horizontally. Typical practical applications of simply supported beams with point loadings include bridges, beams in buildings, and beds of machine tools.

Kinematic Indeterminacy (D_K):

It refers to the number of independent components of joint displacement with the specified set of axes. If the plane frame is extensible, the degree of kinematic indeterminacy = (3j - r) If plane frame is inextensible & unbraced, Degree of kinematic indeterminacy = 3j - (r + m)

And we can determine the Degree of static Indeterminacy only by deducting the number of equilibrium equations from the support reactions. The Degree of kinematic Indeterminacy for a rigid framed structure can be calculated as D_K=3J-R_e.

In the case of two-hinged arch, we have four unknown reactions, but there are only three equations of equilibrium available. Hence, the degree of statical indeterminacy is one for two hinged arch.

The static indeterminacy of a beam is calculated by subtracting the total number of available equilibrium equations from the total support reactions of the beam. It can be classified as external static indeterminacy and internal static indeterminacy.