WHAT IS STATIC INDETERMINACY?
A STRUCTURE IS CONSIDERED STATICALLY INDETERMINATE IF THE EQUATIONS OF STATIC EQUILIBRIUM
(SUM OF FORCES IN X, Y, AND Z DIRECTIONS = 0, SUM OF MOMENTS ABOUT X, Y, AND Z AXES = 0) ARE NOT
SUFFICIENT TO DETERMINE ALL THE UNKNOWN FORCES AND MOMENTS (REACTIONS AT SUPPORTS,
INTERNAL FORCES, ETC.) WITHIN THE STRUCTURE. IN SIMPLER TERMS, THERE ARE MORE UNKNOWNS THAN
INDEPENDENT EQUATIONS.

BY STATIC INDETERMINACY(S.I) CAN FIND WEATHER THE STRUCTURE IS STABLE OR NOT.
S.I = 0, IT MEANS STRUCTURE IS STABLE AND DETERMINATE STUCTURE.
S.I > 0, IT MEANS STRUCTURE IS STABLE AND INDETERMINATE STRUCTURE.
S.I < 0, IT MEANS STRUCTURE IS UNSTABLE.
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GENERAL FORMULA FOR FINDING THE STATICINDETERMINACY
Ds= Dse+ Dsi
Ds = TOTAL STATIC INDETERMINACY
Dse = EXTERNAL INDETERMINACY - NO. OF UNKNOWN REACTIONS
- NO. OF EQUILIBRIUM EQUATIONS(FOR ALL BEAMS, TRUSSES, FRAMES.)
Dsi = INTERNAL INDETERMINACY - VARIES FOR BEAMS, TRUSSES AND FRAMES.
STATIC INDETERMINACY IN BEAMS

EXTERNAL INDETERMINACY
Dse = NO. OF UNKNOWN REACTIONS(R) – NO. OF EQUILIBRIUM EQUATIONS(S)

INTERNAL INDETERMINACY
THERS IS NO INTERNAL INDETERMINACY IN BEAMS. BECAUSE IF THE EXTERNAL REACTION ARE KNOWN WE
CAN FIND MOMENT, SHEAR FORCE IN ANY SECTION. AND THERE IS NO CLOSED ROOFS. SO
Dsi = 0
STATIC INDETERMINACY IN FRAMES

EXTERNAL INDETERMINACY
Dse = NO. OF UNKNOWN REACTIONS(R) – NO. OF EQUILIBRIUM EQUATIONS(S)

INTERNAL INDETERMINACY
Dsi = 3c
c - NO. OF CUTS REQUIRED TO OPEN THE RIGID CLOSED LOOPS
No. of unknown reaction (r) = 2 + 1 = 3
No of equilibrium equation (s) = 3
External indeterminacy(Dse) = 3 – 3 = 0
Internal indeterminacy (Dsi) = 0
(THERE IS NO CLOSEDROOFS)
Total indeterminacy (Ds) = 0 + 0 = 0
Ds = 0, hence the beam is statically determinate
No. of unknown reaction (r) = 3 + 2 = 5
No of equilibrium equation (s) = 3
External indeterminacy (Dse) = 5 – 3 = 2
Internal indeterminacy (Dsi) = 3C = 3*2 = 6
(THERE ARE 2 CLOSEDROOFS)
Total indeterminacy (Ds) = 2 + 6 = 8
Ds = 8, hence the beam is statically Indeterminate of 8 degree
No. of unknown reaction (r) = 3 + 3+2 = 8
No of equilibrium equation (s) = 3
External indeterminacy (Dse) = 8 – 3 = 5
Internal indeterminacy (Dsi) = 3C = 3*2 = 6
(THERE ARE 2 CLOSEDROOFS)
Total indeterminacy (Ds) = 5 + 6 = 11
Ds = 11, hence the beam is statically Indeterminate of 11 degree
No. of unknown reaction (r) = 3 + 2 = 5
No of equilibrium equation (s) = 3
External indeterminacy (Dse) = 5 – 3 = 2
Internal indeterminacy (Dsi) = 3C = 3*2 = 6
(THERE ARE 2 CLOSED ROOFS)
Total indeterminacy (Ds) = 2 + 6 = 8
Ds = 8, hence the beam is statically Indeterminate of 8 degree
No. of unknown reaction (r) = 3 + 3+2 = 8
No of equilibrium equation (s) = 3
External indeterminacy (Dse) = 8 – 3 = 5
Internal indeterminacy (Dsi) = 3C = 3*2 = 6
(THERE ARE 2 CLOSED ROOFS)
Total indeterminacy (Ds) = 5 + 6 = 11
Ds = 11, hence the beam is statically Indeterminate of 11 degree
STATIC INDETERMINACY IN TRUSSES

EXTERNAL INDETERMINACY
Dse = NO. OF UNKNOWN REACTIONS – NO. OF EQUILIBRIUM EQUATIONS

INTERNAL INDETERMINACY
Dsi = m – (2j –3)
m– NUMBER OF MEMBERS IN TRUSS
J – NUMBER OF JOINTS IN TRUSS
No. of unknown reaction (r) = 2 + 1 = 3
No of equilibrium equation (s) = 3
External indeterminacy (Dse) = r – s
=3–3=0
No. of members (m) = 7
No. Of joints (j) = 5
Internal indeterminacy (Dsi) = r – s
=3–3=0
Total indeterminacy (Ds) = 0 + 0 = 0
Ds = 0, hence the beam is statically determinate.