Module 5 · Exercises

Beam behaviour

The same three-step method on a different beam each time. Commit a prediction before you reveal the answer — the explanation compares your choice against a real elastic solve.

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Module 5Level 2deflected shape

Simply supported beam, central point load — deflected shape

A simply supported beam carries a downward point load at mid-span. Which deflected shape is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

deflected shape

Single downward sag, zero at both supports, maximum at mid-span.Option B

deflected shape

The beam arches upward (hogs) between the supports.Option C

deflected shape

The beam stays straight and simply tilts between the supports.Option D

deflected shape

The beam sags but does not return to zero at the right support.

Module 5Level 3bending moment

Simply supported beam, central point load — bending moment

For the same beam, which bending-moment diagram is correct? (Sagging is drawn on the tension side, below the beam.)

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

A triangle: zero at both supports, a single sagging peak under the load.Option B

bending moment (tension side)

A triangle peaking on the hogging (top) side.Option C

bending moment (tension side)

A smooth curve shaped like the deflected beam.Option D

bending moment (tension side)

A constant moment along the whole span.

Module 5Level 2bending moment

Simply supported beam under UDL — bending moment

A simply supported beam carries a full-span uniform load. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

A smooth sagging parabola, zero at the ends, maximum wL²/8 at mid-span.Option B

bending moment (tension side)

A triangle peaking under the middle.Option C

bending moment (tension side)

A parabola on the hogging (top) side.Option D

bending moment (tension side)

A constant moment across the span.

Module 5Level 3shear force

Simply supported beam under UDL — shear force

For the same uniformly loaded beam, which shear-force diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

shear force

A straight line from +wL/2 at the left, through zero at mid-span, to −wL/2 at the right.Option B

shear force

The same line but sloping the opposite way.Option C

shear force

A constant shear along the span.

Module 5Level 2bending moment

Cantilever with a tip load — bending moment

A cantilever built in at the left carries a downward load at its free tip. Which bending-moment diagram is correct? (Hogging is drawn on the top tension side.)

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

Zero at the free tip, growing linearly to a hogging maximum at the fixed end.Option B

bending moment (tension side)

The same magnitude but drawn as sagging.Option C

bending moment (tension side)

A curve shaped like the drooping deflected shape.Option D

bending moment (tension side)

A constant moment along the whole cantilever.

Module 5Level 2deflected shape

Cantilever under UDL — deflected shape

A cantilever carries a uniform load over its full length. Which deflected shape is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

deflected shape

Zero movement and zero slope at the fixing, drooping to a maximum downward deflection at the free tip.Option B

deflected shape

The tip lifts upward instead of drooping.Option C

deflected shape

The beam stays straight and rotates about the fixing.

Module 5Level 4deflected shape

Overhanging beam with a tip load — deflected shape

A beam sits on two supports with a load on the overhang beyond the right support. Which deflected shape is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

deflected shape

The overhang tip drops; the back span between the supports lifts (hogs) as the beam levers over the right support.Option B

deflected shape

The whole beam sags downward between the supports like a simple span.Option C

deflected shape

The beam stays straight and just tips down at the tip.

Module 5Level 4bending moment

Propped cantilever under UDL — bending moment

A cantilever propped by a roller at its far end carries a uniform load. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

Hogging at the fixed end, sagging in the span, passing through zero once (a point of contraflexure).Option B

bending moment (tension side)

The mirror image — sagging at the fixed end, hogging in the span.Option C

bending moment (tension side)

A pure sagging parabola with no hogging, like a simple span.Option D

bending moment (tension side)

A curve copied from the deflected shape.

Module 5Level 3bending moment

Fixed-ended beam under UDL — bending moment

A beam built in at both ends carries a uniform load. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

Hogging at both ends (wL²/12), sagging at mid-span (wL²/24), with two points of contraflexure.Option B

bending moment (tension side)

Sagging at both ends and hogging in the middle.Option C

bending moment (tension side)

A pure sagging parabola, zero at the ends like a simple span.

Module 5Level 4bending moment

Two-span continuous beam under UDL — bending moment

Two equal spans are continuous over a central support and carry a uniform load. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

Sagging in each span, with a hogging peak over the central support.Option B

bending moment (tension side)

Sagging peak over the central support, hogging in the spans.Option C

bending moment (tension side)

Two separate sagging parabolas with zero moment over the middle support.

Module 5Level 5deflected shape

Two-span beam, one span loaded — deflected shape

Only the left span of a two-span continuous beam is loaded. Which deflected shape is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

deflected shape

The loaded span sags; continuity drags the unloaded span into a gentle upward (reverse) curvature.Option B

deflected shape

The loaded span sags and the unloaded span stays perfectly straight and level (as it would with a hinge over the middle support).Option C

deflected shape

Both spans sag equally.

Module 5Level 4bending moment

Beam with an internal hinge — bending moment

A beam has an internal hinge at mid-span. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

The moment is exactly zero at the hinge, hogging towards the fixed end and sagging towards the prop.Option B

bending moment (tension side)

A smooth diagram with a non-zero moment at the hinge.Option C

bending moment (tension side)

Zero moment AND zero shear at the hinge.

Module 5Level 5which impossible

Spot the impossible diagram — moment at a hinge

A solver returns four bending-moment diagrams for this hinged beam. Which one is physically impossible and must be rejected?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

A diagram showing a non-zero bending moment right at the internal hinge.Option B

bending moment (tension side)

A diagram that is zero at the hinge, hogging towards the fixing and sagging towards the prop.Option C

bending moment (tension side)

A diagram that is zero at the hinge but with a smaller sagging span (lighter load).

Module 5Level 4change

Remove the prop — how the deflected shape changes

A propped cantilever loses its end prop (the roller is removed). Which deflected shape describes the changed beam?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

deflected shape

A plain cantilever: single hogging curvature, drooping to a large deflection at the now-free end.Option B

deflected shape

The shape is unchanged because the applied load is the same.Option C

deflected shape

The end still stays at zero deflection even without the prop.

Module 5Level 3shear force

Off-centre point load — shear-force diagram

A simply supported beam carries a point load nearer the left support. Which shear-force diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

shear force

A constant positive value from the left support to the load, a sudden drop of the full load at the load, then a smaller constant negative value to the right support.Option B

shear force

Two equal and opposite constant steps, symmetric about mid-span.Option C

shear force

A single constant value along the whole span.

Module 5Level 3bending moment

Two equal loads at the third points — bending moment

A simply supported beam carries two equal point loads at the third points. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

A trapezoid: rising linearly to the first load, staying constant between the two loads, then falling linearly to the far support.Option B

bending moment (tension side)

A single triangular peak at mid-span.Option C

bending moment (tension side)

A constant moment along the whole span.

Module 5Level 3deflected shape

Cantilever loaded at mid-length — deflected shape

A cantilever carries a point load at its mid-length, with the outer half unloaded. Which deflected shape is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

deflected shape

It curves from the wall to the load, then continues as a straight line to the tip — the unloaded outer half carries no moment, so it does not bend.Option B

deflected shape

It curves continuously all the way to the tip, bending most near the free end.Option C

deflected shape

The tip stays at zero while the middle droops.

Module 5Level 2bending moment

Cantilever loaded at mid-length — bending moment

For the same cantilever loaded at mid-length, which bending-moment diagram is correct? (Hogging is drawn on the tension — top — side.)

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

A hogging maximum at the wall, falling linearly to zero at the load, and exactly zero along the unloaded outer half.Option B

bending moment (tension side)

The same diagram drawn as sagging.Option C

bending moment (tension side)

A constant moment along the whole cantilever.

Module 5Level 4bending moment

Built-in beam, central point load — bending moment

A beam built in at both ends carries a central point load. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

Hogging at both fixed ends and sagging under the load, crossing zero twice (two points of contraflexure).Option B

bending moment (tension side)

A single sagging triangle, exactly like a simply supported beam.Option C

bending moment (tension side)

Purely hogging across the whole span.

Module 5Level 2deflected shape

Uniformly loaded simple span — deflected shape

A simply supported beam carries a uniform load over its whole length. Which deflected shape is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

deflected shape

A smooth symmetric sag, zero at both supports and a single downward maximum at mid-span.Option B

deflected shape

The beam hogs upward between the supports.Option C

deflected shape

The beam stays straight and tilts between the supports.

Module 5Level 4deflected shape

Load on one half only — deflected shape

A simply supported beam is loaded by a uniform load over its LEFT half only. Which deflected shape is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

deflected shape

It sags with its deepest point shifted toward the loaded (left) half, not at mid-span, but still returns to zero at both supports.Option B

deflected shape

The deepest point is exactly at mid-span, as if fully loaded.Option C

deflected shape

The unloaded half lifts above the supports.

Module 5Level 3shear force

Cantilever under UDL — shear-force diagram

A cantilever carries a uniform load over its whole length. Which shear-force diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

shear force

Largest at the wall, equal to the total load, and falling linearly to zero at the free tip.Option B

shear force

Largest at the free tip and zero at the wall.Option C

shear force

Constant along the whole cantilever.

Module 5Level 4bending moment

Propped cantilever — where does the moment change sign?

A propped cantilever (fixed at one end, propped by a roller at the other) carries a uniform load. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

bending moment (tension side)

Hogging at the fixed end, sagging in the span, crossing zero once at a point of contraflexure nearer the fixed end.Option B

bending moment (tension side)

A pure sagging parabola with no hogging, like a simple span.Option C

bending moment (tension side)

Hogging along the whole span with no sagging region.

Module 5Level 3deflected shape

Propped cantilever with a central load — deflected shape

A propped cantilever carries a point load at mid-span. Which deflected shape is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, the load path and compatibility — not the one that looks familiar.

Option A

deflected shape

It leaves the fixing horizontally, sags in the span and returns to zero at the prop, with a gentle reverse of curvature between the two.Option B

deflected shape

The propped end lifts above its support.Option C

deflected shape

It leaves the fixing at a steep slope, like a pinned end.

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