Module 6 · Exercises

Continuous beams

Continuity 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 6Level 3bending moment

Three-span continuous beam under UDL — bending moment

Three equal spans are continuous over the interior supports 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 both interior supports.Option B

bending moment (tension side)

Sagging peaks over the interior supports, hogging in the spans.Option C

bending moment (tension side)

Three separate sagging parabolas, zero moment over both interior supports.

Module 6Level 3which impossible

Two-span continuous beam — where the load goes

Two equal spans (each 6 m) are continuous over the central support and carry a uniform load of 8 kN/m. A tributary-area estimate gives the centre wL=48 kN and each end wL/2=24 kN. Which statement about the real reactions 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 central support carries about 60 kN — a quarter more than the tributary estimate — and each end support carries about 18 kN.Option B

bending moment (tension side)

All three supports carry the same 48 kN, as the tributary estimate says.Option C

bending moment (tension side)

The end supports carry the most, because they are furthest from the middle.

Module 6Level 4change

Add a central prop to a simple beam

A simply supported beam under a uniform load has a new prop added at mid-span. Which bending-moment diagram 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

bending moment (tension side)

Sagging in each half with a new hogging peak over the central prop — the beam is now continuous over three supports.Option B

bending moment (tension side)

The single sagging parabola is unchanged, just smaller, because the load is the same.Option C

bending moment (tension side)

A pure hogging diagram over the whole span.

Module 6Level 4change

Remove an interior support

One interior support is removed from a three-span continuous beam under uniform load. What happens?

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 two spans either side merge into one long span, which deflects much more and throws extra hogging onto the remaining interior support.Option B

deflected shape

Nothing changes elsewhere; only the removed support's load vanishes.Option C

deflected shape

The beam becomes a mechanism and collapses.

Module 6Level 5which impossible

An interior support settles — with no applied load

An interior support of a continuous beam settles downward. There is no applied load on the beam at all. Which statement 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)

Bending moments and reactions develop anyway, because continuity resists the imposed movement.Option B

bending moment (tension side)

Nothing happens: with no load there can be no moment — the diagram is flat at zero.Option C

bending moment (tension side)

The settlement bends the beam uniformly, giving the same constant moment all along.

Module 6Level 4bending moment

Unequal spans under the same load

A continuous beam has a short span (3 m) and a long span (6 m) over a shared interior support, both under the same 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)

Both spans have a sagging region, much larger in the long span. The short span hogs over most of its length, and the shared support has one continuous hogging moment.Option B

bending moment (tension side)

The two spans give equal and opposite moments, because the load per metre is the same.Option C

bending moment (tension side)

Two separate parabolas with no hogging over the interior support.

Module 6Level 4bending moment

A continuous beam with an internal hinge

A continuous beam has an internal hinge partway along the last 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, with hogging over the interior support and sagging in the spans elsewhere.Option B

bending moment (tension side)

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

bending moment (tension side)

Zero moment everywhere in the hinged span.

Module 6Level 5which impossible

Loading the middle span — do the ends lift?

In a three-span continuous beam, only the middle span is loaded. What happens at the two end supports?

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 end spans are pulled upward by continuity, so the end reactions act downward — and a bearing that cannot pull would lift off.Option B

deflected shape

The end supports carry their usual upward share of the load.Option C

deflected shape

The end spans stay perfectly straight and level.

Module 6Level 2bending moment

Two equal spans 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 single hogging peak over the central support — the two humps and one trough of a continuous beam.Option B

bending moment (tension side)

Two separate sagging parabolas, with zero moment over the central support.Option C

bending moment (tension side)

Hogging in the spans with a sagging peak over the support.

Module 6Level 3deflected shape

Two equal spans under UDL — deflected shape

For the same two-span beam under a uniform load, 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

Each span sags to a maximum, held to zero at all three supports, with the curvature reversing (a contraflexure) either side of the central support.Option B

deflected shape

The beam hogs upward in both spans.Option C

deflected shape

The central support point floats below the beam line.

Module 6Level 3bending moment

Load on one span only — bending moment

Only the LEFT span of a two-span continuous beam 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)

The loaded span sags with a hogging moment over the central support that reaches into the unloaded span as a smaller hogging moment.Option B

bending moment (tension side)

Zero moment everywhere in the unloaded span, since it carries no load.Option C

bending moment (tension side)

A sagging peak over the central support.

Module 6Level 4deflected shape

Does the unloaded span lift?

With only the left span loaded, what does the unloaded right span do?

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 is dragged into an upward (reverse) curvature and lifts above its unloaded rest line — continuity rotates the central support, raising the far span.Option B

deflected shape

It stays perfectly straight and level, because it carries no load.Option C

deflected shape

It sags downward just like the loaded span.

Module 6Level 4deflected shape

Load the middle span of three

In a three-span continuous beam, only the MIDDLE span is loaded. What do the two outer spans do?

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 middle span sags, and continuity lifts both outer spans into upward reverse curvature — their far ends can even tend to lift off.Option B

deflected shape

The outer spans stay flat and level, carrying nothing.Option C

deflected shape

The outer spans sag downward with the middle span.

Module 6Level 3change

Remove the central support

The central support of a two-span continuous beam is removed, leaving a single span of double the length. Which bending-moment diagram 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

bending moment (tension side)

A single large sagging parabola over the full length, with no hogging anywhere — and a far larger peak moment than before.Option B

bending moment (tension side)

The same two-hump, one-trough diagram as before, only slightly larger.Option C

bending moment (tension side)

A hogging diagram, because the beam now spans further.

Module 6Level 4bending moment

Unequal spans — where is the hogging worst?

A continuous beam has a short left span and a long right span under the same 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 over the interior support with a large sagging peak in the long span; the short span may even hog for most of its length.Option B

bending moment (tension side)

The two spans have identical, symmetric moment diagrams.Option C

bending moment (tension side)

The short span carries the larger sagging moment.

Module 6Level 4bending moment

Overhangs both ends — bending moment

A uniformly loaded beam rests on two supports set in from the ends, so it overhangs at both ends. 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 over each support (from the overhang load) and sagging in the middle span, crossing zero twice.Option B

bending moment (tension side)

A single sagging parabola over the whole length.Option C

bending moment (tension side)

Hogging over the whole length.

Module 6Level 3shear force

Two equal spans under UDL — shear-force diagram

For the two-span continuous beam under a uniform load, 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

Shear falls linearly through each span and jumps upward at the central support by its large reaction — the jump there is the biggest of the three.Option B

shear force

A single straight line from one end of the beam to the other.Option C

shear force

Constant shear along the whole beam.

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