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Module 4 · Exercises

Stiffness

Predict before you reveal — the explanation compares your choice against the structural model.

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Module 4Level 3change and sensitivity

Which column carries more of a sideways load?

Two columns, tied at the top by a rigid beam, share a horizontal load. The left column is much stiffer than the right. Which carries more of the load?

Predict first, then reveal

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

AThe stiffer (left) column — the rigid beam forces both tops to move together, and the stiffer column needs a larger force to reach that movement.BThe flexible (right) column, because it gives way and takes up the load.CThey share it equally, because the beam ties them together.

Module 4Level 3change and sensitivity

Take one stiffness to zero

In the two-column arrangement, the right column is made softer and softer until its stiffness is almost nothing. What happens to the load sharing?

Predict first, then reveal

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

AThe left column carries almost all the load; the near-zero-stiffness column carries almost none.BThe soft column carries almost all the load, because it deflects most.CThe sharing stays 50:50 whatever the stiffness.

Module 4Level 4which impossible

Force from movement, with no load

A continuous beam has no load on it at all, but one of its supports settles downward. Does it develop bending moment?

Predict first, then reveal

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

AYes — the beam is over-constrained, so forcing a support out of position bends it. Compatibility, not applied load, produces the moment.BNo — with no applied load there can be no bending moment.COnly if the beam is also carrying load at the same time.

Module 4Level 4change and sensitivity

When geometry alone cannot answer

Two parallel members share a load between the same two points. You are told the geometry but nothing about the members' stiffnesses. Can you say how the load is shared?

Predict first, then reveal

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

ANo — sharing between redundant parallel paths depends on their relative stiffness, which is not given. The honest answer is that it cannot be determined from geometry alone.BYes — they share equally, because they connect the same two points.CYes — the shorter path always takes more load.

Module 4Level 3change and sensitivity

Does a continuous beam share load equally?

A two-span continuous beam carries a uniform load over both spans. A tributary-area estimate would give each of the three supports an equal share. Is that right?

Predict first, then reveal

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

ANo — continuity draws extra load to the interior support, which carries about 1.25 wL, more than a tributary estimate; the end supports carry less.BYes — the supports are evenly spaced, so they share equally.CNo — the end supports carry more, because they are at the extremities.

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