Qualitative behaviour of frames exercises

Module 7Level 3change

Fix the bases of a swaying portal

A pinned-base portal frame sways under a horizontal load. Its bases are then changed to fully fixed. What happens to the sway?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Deflected shape

The frame sways much less, and the columns bend in double curvature with an inflection point partway up.Option B

Deflected shape

The sway is unchanged, because the load is the same.Option C

Deflected shape

The frame sways even more, because fixing the bases adds load.

Module 7Level 3bending moment

Do the columns bend under gravity load?

A portal frame carries a uniform gravity load on its beam only. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Bending moment

The beam sags between hogging knees, and the columns also carry bending moment — the rigid joints transfer it around the corners.Option B

Bending moment

Only the beam bends; the columns carry pure axial force with no moment at all.Option C

Bending moment

The beam hogs in the middle and sags at the knees.

Module 7Level 4deflected shape

Does a symmetric portal sway under gravity?

A symmetric portal frame carries a symmetric gravity load on its beam. Which deflected shape is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Deflected shape

No sway: the beam sags symmetrically and the columns bend outward a little, but the frame does not lean to either side.Option B

Deflected shape

The frame sways to one side as it takes up the load.Option C

Deflected shape

The beam sags but the columns stay perfectly straight and vertical.

Module 7Level 4bending moment

Bending moment of a fixed-base portal under horizontal load

A fixed-base portal frame is pushed sideways by a horizontal load. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Bending moment

Moment at the fixed bases and at the knees, with the columns bending in double curvature (the moment changes sign up the column).Option B

Bending moment

Zero moment at the bases, exactly like a pinned-base frame.Option C

Bending moment

The moments are the mirror image, hogging where the frame really sags.

Module 7Level 4change

Add a diagonal brace to a swaying frame

A pinned-base portal sways badly under horizontal load. A diagonal brace is added across the frame. What happens?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Deflected shape

The sway almost disappears: the brace carries the horizontal load as axial force through a triangulated path.Option B

Deflected shape

The sway is unchanged, because the brace only adds weight.Option C

Deflected shape

The frame sways the other way now.

Module 7Level 3bending moment

A load on the arm of a cantilever frame

An L-shaped cantilever frame — a fixed column with a horizontal arm — carries a downward load at the tip of the arm. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Bending moment

Moment grows along the arm to the corner and continues down the whole column to the fixed base.Option B

Bending moment

Only the arm bends; the column carries pure axial force with no moment.Option C

Bending moment

The moment is largest at the free tip and zero at the base.

Module 7Level 3deflected shape

How a pinned-base portal sways

A portal frame with pinned bases carries a horizontal load at the top of one column. Which deflected shape is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Deflected shape

The whole frame leans in the direction of the load; both columns bend in single curvature and the beam stays roughly straight as it rides across.Option B

Deflected shape

The frame does not move, because the beam is rigid.Option C

Deflected shape

The frame leans against the load, in the opposite direction.

Module 7Level 3bending moment

Bending moment in a swaying portal

For the pinned-base portal under a horizontal load, which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Bending moment

Zero moment at each pinned foot, rising up each column to a peak at the knee, and carried across the beam — the columns clearly bend.Option B

Bending moment

Moment only in the beam; the columns carry pure axial force.Option C

Bending moment

The largest moment is at the pinned feet.

Module 7Level 4deflected shape

Column shape of a fixed-base portal

A portal frame with FIXED bases sways under a horizontal load. What shape do the columns take?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Deflected shape

Each column bends in double curvature — an S-shape with an inflection point partway up — because both the base and the knee resist rotation.Option B

Deflected shape

Each column bends in a simple single curve, like a pinned-base portal.Option C

Deflected shape

The frame does not sway at all, because the bases are fixed.

Module 7Level 4bending moment

Where the moment goes in a fixed-base portal

For the fixed-base portal under a horizontal load, which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Bending moment

Moment appears at the fixed feet AND at the knees, with opposite signs on each column — so the moment reverses partway up.Option B

Bending moment

Zero moment at the feet, exactly like a pinned base.Option C

Bending moment

The columns carry no moment; only the beam bends.

Module 7Level 4bending moment

Gravity on a pinned-base portal — bending moment

A portal frame with pinned bases carries a uniform gravity load on its beam. Which bending-moment diagram is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Bending moment

The beam sags in the middle and hogs at the knees, and that knee moment runs down the columns to zero at the pinned feet.Option B

Bending moment

Only the beam carries moment; the columns are moment-free struts.Option C

Bending moment

The beam hogs in the middle and sags at the knees.

Module 7Level 3deflected shape

Deflection of an L-shaped frame

An L-shaped frame has a fixed column with a horizontal arm cantilevering off the top. A load hangs at the arm tip. Which deflected shape is correct?

the structure

Predict first, then reveal

Choose the response that obeys the supports, joint continuity and equilibrium — not the one that looks familiar.

Option A

Deflected shape

The arm tip drops sharply, and the rigid joint carries that rotation into the column, which bends over towards the load.Option B

Deflected shape

Only the arm droops; the column stays perfectly vertical.Option C

Deflected shape

The arm tip lifts upward.