A structure is statically indeterminate when the number of unknown reactions and internal forces exceeds the number of independent equilibrium equations (ΣFₓ = 0, ΣFᵧ = 0, ΣM = 0 for 2D; six equations for 3D).
Degree of Indeterminacy = Total unknowns − Number of independent equilibrium equations.
Examples: Continuous beams, fixed-end beams, rigid frames, arches, and trusses with redundant members.
Advantages over determinate structures:
Disadvantages:
Draw influence lines for reaction, shear, and moment at various points in a two-span continuous beam.
Statically indeterminate structures are those in which static equilibrium equations alone are insufficient to determine internal forces and reactions. Additional compatibility conditions (deformations and material/geometry relationships) are required. Chu Kia Wang’s PDF (a common textbook/lecture-note source) offers clear explanations and worked examples; this post summarizes key concepts, methods, and example problems to help readers understand and apply the material. statically indeterminate structures chu kia wang pdf
Work through problems with one, two, and three redundancies. Use symmetry to simplify.
Chu Kia Wang (1916–2000) was a renowned professor of civil engineering at the University of Idaho and later at the University of Kansas. He authored several influential textbooks, but his work on indeterminate structures stands out.
Wang’s philosophy was simple: bridge theory with practice. He recognized that students often mastered the mathematical tricks of slope-deflection or moment distribution but failed to understand how a real building or bridge actually "feels" loads. His writing style is direct, example-driven, and meticulous—qualities that explain why his book has remained in demand long after its last printing. A structure is statically indeterminate when the number
The full title usually appears as:
Statically Indeterminate Structures (McGraw-Hill, various editions, notably 1953, 1963, and later reprints)
Wang’s treatment of this iterative method is a highlight. He explains distribution factors, carry-over moments, and how to handle unbraced frames (sidesway). The step-by-step tabular format he uses has been copied by many later authors. Disadvantages : Draw influence lines for reaction, shear,
Consider a two-span continuous beam, fixed at left, simply supported at two interior points, and free at right end.