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The degree of static indeterminacy of a rigid jointed frame PQR supported as shown in the figure is

The degree of static indeterminacy of a rigid jointed frame PQR supported as shown in the figure is Correct Answer Zero

Concept

Method 1: Using basic concept

The degree of static indeterminacy means no of unknowns beyond available equation of equilibrium equations.

Segment RS is cable and cable can resist only tensile force, so there will be one unknown at joint R.

Further, Joint P is hinged and therefore, there will be only two reactions in x and y direction as shown in figure:

Total unknown = 1 (at Joint R) + 2 (at Joint P) = 3

For frame PQR, there are 3 Equations of Equilibrium available as shown in above figure, by using these equation these 3 unknown can be easily predicted.

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Equilibrium equation:

∑Fx = 0, ∑Fy = 0, ∑Mp = 0

∴ Ds = 3 – 3 = 0

 

Method 2: Using direct formula:

Degree of Static Indeterminacy (Ds):

Ds = Dse + Dsi

Dse = Degree of external static indeterminacy.

Dsi = Degree of internal static indeterminacy.

Dse = Support Reactions – Number of Equilibrium equations

Dsi = 3  C – R

C = No of closed loops

R = No of releases = m - 1

Calculation:

No of reactions = 2 + 2 = 4 (2 reactions at joint S and P each)

No of equilibrium reactions = 3

Dse = 4 - 3 = 1

No of closed loops, C = 0

Releases

Moment releases at joint R = 2 - 1 = 1

Dsi = 3  C – R = 3  – 1 = -1

Ds = Dse + Dsi = 1 - 1 = 0

∴ Static Indeterminacy, D­s = 0

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