Civil Engineering Essentials

A structure where all internal forces and reactions can be determined using equilibrium equations alone (ΣF=0, ΣM=0), without needing compatibility or material properties.

The number of redundant forces beyond those solvable by static equilibrium; calculated as the total unknowns minus the number of independent equilibrium equations.

It solves for member end moments in statically indeterminate beams and frames by iteratively distributing unbalanced moments at joints until equilibrium is reached.

The stiffness factor is k = 4EI/L for a far-end fixed member or k = 3EI/L for a far-end pinned member, where E is modulus, I is moment of inertia, and L is length.

It is 0.5 for a member with a fixed far end, meaning half the distributed moment at the near joint is carried over to the far joint.

For linear elastic structures, the total response (deflection, moment, shear) caused by multiple loads equals the sum of responses caused by each load acting independently.

It is used to calculate deflections in trusses and beams by applying a virtual unit load at the point of desired deflection and integrating internal virtual work.

A location in a structural member where the full plastic moment (Mp) is reached, allowing rotation without additional moment resistance, enabling redistribution of moments.

It is KL/r, where K is the effective length factor, L is the unbraced length, and r is the radius of gyration; it determines whether a column fails by buckling or crushing.

P_cr = π²EI / (KL)², applicable to long, slender columns in the elastic range where buckling governs over material yielding.

The ratio of the weight of water to the weight of cement in a mix; lower ratios produce stronger, more durable concrete but reduce workability.

It is the standard design strength (f'c) measured by crushing a cylinder or cube after curing for 28 days under controlled conditions.