Stiffness method — exercises | Queensferry

Module 12Level 3reactions and load path

What are the unknowns?

In the stiffness (displacement) method, what quantities are taken as the unknowns to solve for?

Predict first, then reveal

Reason from the supports, the movement and equilibrium — not from what looks familiar.

AThe joint displacements and rotations — the method solves for how far each joint moves, then recovers the forces.BThe redundant forces, chosen by releasing restraints.CThe support reactions, found directly from equilibrium.

Module 12Level 3change and sensitivity

Lock the joints first

The stiffness method begins by locking every joint against rotation. What does this first step give you?

Predict first, then reveal

Reason from the supports, the movement and equilibrium — not from what looks familiar.

AThe fixed-end moments: with every joint clamped, each member is fixed-ended, and its end actions are known standard results.BThe final answer — the locked state is the real response.CNothing useful; locking joints removes all the moments.

Module 12Level 3change and sensitivity

Sharing an out-of-balance moment

Two members of the same EI but different length meet at a rigid joint, both with fixed far ends. An out-of-balance moment at the joint is shared between them. Which takes more?

Predict first, then reveal

Reason from the supports, the movement and equilibrium — not from what looks familiar.

AThe shorter member — its rotational stiffness 4EI/L is larger, so it attracts the larger share of the moment.BThe longer member, because it is more flexible and gives way.CThey share it equally, because the EI is the same.

Module 12Level 4change and sensitivity

Why is the stiffness matrix symmetric?

In the assembled global stiffness matrix K, the entry Kᵢⱼ equals Kⱼᵢ for every i and j. What principle does that symmetry express?

Predict first, then reveal

Reason from the supports, the movement and equilibrium — not from what looks familiar.

AMaxwell's reciprocal theorem — the force at i from a unit displacement at j equals the force at j from a unit displacement at i, for a linear elastic structure.BA convenient choice of numbering; renumber and it becomes unsymmetric.CIt is a coincidence of the beam element and does not hold generally.

Module 12Level 3software check

Why software uses the stiffness method

Analysis programs are built on the stiffness method rather than the flexibility (force) method. What is the main reason?

Predict first, then reveal

Reason from the supports, the movement and equilibrium — not from what looks familiar.

AIt is mechanical: it needs no judgement about which redundant to release. It restrains what is restrained, solves Kd = f, and recovers the rest — the same steps for any structure.BIt is always more accurate than the flexibility method.CIt avoids ever forming a matrix.