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Module 8 · Exercises

Trusses, arches and cables

Read which members pull and which push before you reveal the answer — every force pattern is from a real solve.

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Module 8Level 2internal force diagram

Rafters and tie in a roof truss

A simple roof truss carries a downward load at its apex. Which members are in compression and which in tension?

Predict first, then reveal

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

AThe sloping rafters are in compression; the bottom tie is in tension, holding the supports together against the outward thrust.BThe rafters are in tension and the tie is in compression.CEvery member is in tension, because the load pulls down on the whole truss.

Module 8Level 3internal force diagram

The member carrying nothing

In the king-post truss with the load at the apex, one member carries no force at all. Which one, and why?

Predict first, then reveal

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

AThe central vertical post — at the bottom joint the two tie halves are collinear and nothing else pulls vertically, so the post is a zero-force member.BThe bottom tie, because horizontal members never carry force.CNone — every member in a triangulated truss carries force.

Module 8Level 3change and sensitivity

Move the load to the bottom joint

The load is moved from the apex to the bottom-middle joint (where the post meets the tie). What happens to the previously zero-force post?

Predict first, then reveal

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

AIt springs into action: the post now carries the load in tension, hanging the bottom joint from the apex.BIt stays a zero-force member, because it was zero before.CIt goes into compression, pushing the joint down.

Module 8Level 3internal force diagram

Chords of a cantilever truss

A parallel-chord truss cantilevers from a wall and carries a downward load at its free end. Which chord is in tension — the top or the bottom?

Predict first, then reveal

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

AThe top chord is in tension and the bottom chord in compression — the cantilever hogs, stretching the top fibre.BThe bottom chord is in tension, because the load pulls down on it.CBoth chords are in tension, since the whole truss is pulled down.

Module 8Level 3change and sensitivity

Remove the tie

The bottom tie of the roof truss is removed. The rafters remain, on a pin and a roller. What happens?

Predict first, then reveal

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

AThe rafters' outward thrust is no longer held, so the roller support spreads outward — the tie was resisting the horizontal thrust, and something else must now do so.BNothing changes — the rafters carry the load on their own.CThe rafters go into tension instead.

Module 8Level 2internal force diagram

How a cable carries a load

A cable is anchored at both ends and carries a single point load. How does it carry the load, and what shape does it take?

Predict first, then reveal

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

AIn pure tension — a cable cannot push or bend, so it forms straight segments meeting at the load (the funicular shape). Inverted, that shape is an arch in pure compression.BIn bending, like a beam, since it spans between the anchors.CIn compression, because the load pushes down on it.

Module 8Level 1internal force diagram

The one tension member in a triangle

A single triangle carries a downward load at its apex on a pin and a roller. Its members are labelled A, B and C. Which member is in tension?

Predict first, then reveal

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

AMember C, the bottom horizontal — it is the tie, stretched as the two rafters push their supports apart.BMember A, the left rafter, because the load leans onto it first.CAll three members are in tension, because the load pulls the whole triangle down.

Module 8Level 2internal force diagram

Top and bottom chords of a Warren truss

A Warren truss on a pin and a roller carries a downward load at its bottom-middle joint. Is the top chord in tension or compression — and the bottom chord?

Predict first, then reveal

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

AThe top chord is in compression and the bottom chord in tension — the truss sags, so it behaves like a beam with a compression top and a tension bottom.BThe top chord is in tension and the bottom chord in compression.CBoth chords are in compression because they run along the span.

Module 8Level 3internal force diagram

The diagonal pattern in a Warren truss

In the same Warren truss (load at the bottom-middle joint), the four diagonals are labelled D, E, F and G from left to right. Which are in compression and which in tension?

Predict first, then reveal

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

AThe outer diagonals D and G are in compression; the inner diagonals E and F are in tension — the outer pair prop up the reactions, the inner pair hang the load.BAll four diagonals are in compression, since diagonals brace against sway.CThe inner diagonals E and F are in compression and the outer D and G in tension.

Module 8Level 2internal force diagram

State of a single diagonal (member D)

In the Warren truss loaded at its bottom-middle joint, what is the state of member D — the diagonal that rises from the pinned support to the first top joint?

Predict first, then reveal

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

ACompression — member D is the strut that carries the support reaction up into the top chord.BTension, because it is a diagonal and diagonals are ties.CZero force, because no load is applied at its ends.

Module 8Level 4change and sensitivity

Move the load to the top joints

The same Warren truss is now loaded at its two TOP joints instead of the bottom-middle joint. What happens to the two inner diagonals, E and F?

Predict first, then reveal

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

AThey fall to zero force — with no load hung at the bottom-middle joint, the two inner diagonals have nothing to carry there.BThey stay in tension exactly as before, since the total load is unchanged.CThey reverse into compression because the load is now above them.

Module 8Level 1internal force diagram

Is the rafter pushing or pulling?

In the loaded triangle, consider member A — the left rafter running from the pinned support up to the apex. Is it in tension, compression, or carrying no force?

Predict first, then reveal

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

ACompression — the apex load bears down the rafter towards the support, squeezing it along its length.BTension, because the apex is being pulled down and drags the rafter with it.CZero force, because the load is applied at the apex, not on the rafter itself.

Module 8Level 3internal force diagram

Diagonals of a Pratt truss

A Pratt truss carries gravity loads at its bottom joints. Its two web diagonals slope DOWN towards mid-span (labelled L and M). Are they in tension or compression?

Predict first, then reveal

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

ATension — a Pratt diagonal slopes down toward mid-span, so it carries the panel shear by pulling; the vertical posts then take the compression.BCompression, because diagonals always act as struts.CZero force, since the verticals carry all the shear.

Module 8Level 4internal force diagram

The idle post over mid-span

In the Pratt truss one vertical member carries no force at all under this symmetric loading. Which one, and why? (Member J is the vertical at the top-centre joint.)

Predict first, then reveal

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

AMember J, the central vertical — at the unloaded top-centre joint the two top-chord segments are collinear, so the branching vertical carries nothing.BNo member is idle — a fully triangulated truss loads every bar.COne of the end posts, because it only leans against the support.

Module 8Level 3internal force diagram

Which member works hardest?

In the Pratt truss under gravity, which members carry the largest force — and in what sense? (G and H are the inclined end posts by the supports.)

Predict first, then reveal

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

AThe inclined end posts G and H, in compression — they carry the full support reaction straight into the truss.BThe central vertical, in tension, because it is at mid-span where the moment is largest.CThe web diagonals, in compression, because diagonals carry the shear.

Module 8Level 3internal force diagram

Diagonals of a Howe truss

A Howe truss has the SAME chords and verticals as a Pratt truss, but its diagonals slope the opposite way — UP towards mid-span. Under the same gravity load, are the diagonals in tension or compression?

Predict first, then reveal

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

ACompression — reversing the diagonal's slope turns it into a strut, so the Howe diagonals push while the verticals now pull.BTension, exactly like the Pratt truss, because the load is the same.CZero force, because the two truss types cancel out.

Module 8Level 4change and sensitivity

Why choose Pratt over Howe?

Pratt and Howe trusses carry the same gravity load with identical chords — only the diagonal direction differs. Why is the Pratt arrangement often preferred for a steel roof or bridge?

Predict first, then reveal

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

AIn a Pratt truss the long diagonals are in tension and only the short verticals are in compression — so the compression members are short and less likely to buckle.BThe Pratt truss carries more load because tension is stronger than compression.CThe Pratt truss uses fewer members, so it is lighter.

Module 8Level 2internal force diagram

Rafters and tie of a Fink roof truss

A Fink roof truss carries the roof load at the joints along its sloping rafters. Are the rafters (A–D) in tension or compression, and the bottom tie (E, F)?

Predict first, then reveal

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

AThe rafters are in compression and the bottom tie in tension — the rafters carry the roof load down to the eaves, thrusting outward, and the tie holds the eaves together.BThe rafters are in tension and the tie in compression, because the roof hangs from the ridge.CEvery member is in compression, since the whole roof pushes down.

Module 8Level 3internal force diagram

The central post of the Fink truss

In the Fink truss the central vertical (member I) runs from the apex down to the middle of the bottom tie. Under the roof load, is it in tension, compression, or zero?

Predict first, then reveal

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

ATension — the central post hangs the middle of the long bottom tie up towards the apex, stopping it from sagging.BCompression, because a vertical post is always a strut.CZero force, because it sits on the axis of symmetry.

Module 8Level 3internal force diagram

Which leg of a wind-loaded tower is in tension?

A braced tower is pinned at both feet and pushed sideways by a wind load at the top. Which vertical leg goes into tension — the windward side (where the wind hits) or the leeward side?

Predict first, then reveal

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

AThe windward leg is in tension — the wind tends to overturn the tower, lifting the windward foot, so that leg is pulled to hold it down.BThe leeward leg is in tension, because the wind pushes the tower towards it.CBoth legs are in compression, since the tower stands on both feet.

Module 8Level 3internal force diagram

What the tower's diagonal braces do

The tower has a single diagonal brace in each storey (members G and H). Under the sideways wind load, what do these diagonals carry?

Predict first, then reveal

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

AThey carry the horizontal wind shear down the tower, acting here as tension diagonals across each storey.BNothing — the vertical legs carry all the wind on their own.CThey carry the vertical weight of the tower down to the feet.

Module 8Level 4internal force diagram

An idle leg segment at the loaded corner

At the top corner where the wind load is applied, one vertical member (B, the upper windward leg) carries no force. Why?

Predict first, then reveal

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

AAt that corner the only load is horizontal, and B is the only vertical member there — so vertical equilibrium forces its axial force to zero.BBecause it is on the windward side, which never carries load.CBecause the wind load is small; a larger wind would load it.

Module 8Level 3internal force diagram

Two idle members in a single braced panel

A square panel is braced by one diagonal and loaded at a single corner. Two of its four edge members carry no force. Which reasoning finds them?

Predict first, then reveal

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

AAt the unloaded corners, two non-collinear members meet with nothing else pulling on them, so each such pair must both be zero.BThe two horizontal members are zero because horizontal members never carry load.CNo member is zero — a braced panel loads all its edges.

Module 8Level 2principle

Why truss members carry axial force only

An idealised truss member carries only axial force — tension or compression, never bending. What two idealisations make this true?

Predict first, then reveal

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

AThe joints are frictionless pins (they transmit no moment) and every load is applied only at the joints (so no member carries a transverse load along its length).BThe members are very stiff, so they cannot bend.CThe members are all triangulated, which removes bending.

Module 8Level 3principle

A load applied between the joints

A load is hung from the MIDDLE of a truss member, not at a joint. What happens to that member — and to the truss idealisation?

Predict first, then reveal

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

AThat member now bends like a little beam as well as carrying axial force — it is no longer a pure two-force member, and the simple truss reading breaks down for it.BNothing changes — the load just splits to the nearest joints and stays axial.CThe whole truss collapses, because trusses cannot take off-joint loads.

Module 8Level 3principle

Where to start the method of joints

You want to find the bar forces of the Warren truss by the method of joints. Which joint should you resolve FIRST, and what does it give you?

Predict first, then reveal

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

AStart at a support joint, where only two members meet — two equilibrium equations then solve those two bar forces directly (here the bottom chord in tension and the end diagonal in compression).BStart at the most heavily loaded joint in the middle, where the action is.CStart anywhere; the order makes no difference to the method.

Module 8Level 4principle

Finding one chord force with a single cut

You need only the mid-span bottom-chord force of the Pratt truss, without solving every joint. How does the method of sections get it in one step?

Predict first, then reveal

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

ACut through three members including that chord, then take moments about the joint where the other two cut members meet — only the wanted chord force appears, and it comes out in tension.BCut the chord and read its force from the vertical equilibrium of the cut.CYou cannot; the method of sections only gives diagonals, never chords.

Module 8Level 3principle

Counting bars, joints and reactions

A pin-jointed plane truss has m members, r support reactions and j joints. What does the count m + r = 2j tell you?

Predict first, then reveal

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

AIt is the condition for statical determinacy: two equilibrium equations per joint (2j) are exactly matched by the unknown bar and reaction forces (m + r).BIt guarantees the truss is stable and cannot form a mechanism.CIt gives the maximum load the truss can carry.

Module 8Level 3principle

The thrust of an arch

An arch carries its load in compression, like an inverted cable. What does it do at its supports that a simply supported beam does not?

Predict first, then reveal

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

AIt pushes outward and downward on its supports — a horizontal thrust — which must be resisted by abutments or a tie, or the arch spreads and flattens.BNothing different — it gives purely vertical reactions like a beam.CIt pulls its supports inward, like a cable.

Module 8Level 3change and sensitivity

A cable under a spread load

The single point load on a cable is replaced by a uniform load spread along the span. What shape does the cable now take, and how does it carry the load?

Predict first, then reveal

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

AIt hangs as a smooth parabola — the funicular shape of a uniform load — carrying everything in tension; inverted, that parabola is the ideal compression arch.BIt stays in straight segments, because a cable can only be straight.CIt takes a circular arc, the strongest shape.

Module 8Level 3principle

Why compression members deserve respect

Two truss members carry the same size of force — one in tension, one in compression. Why is the compression member usually the one that governs the design?

Predict first, then reveal

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

AA compression member can buckle — deflect sideways and fail well below its squash strength — and the risk grows with length and slenderness, whereas a tension member simply carries its force.BCompression is a weaker kind of stress than tension in steel.CCompression members carry larger forces than tension members.

Module 8Level 2internal force diagram

State of an inner diagonal (member E)

In the Warren truss loaded at its bottom-middle joint, what is the state of member E — the inner diagonal running from the first top joint DOWN to the loaded bottom joint?

Predict first, then reveal

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

ATension — member E helps hang the loaded bottom joint up from the top chord, so it is being stretched.BCompression, because it is a diagonal carrying load down to a support.CZero force, since the load is applied at its lower end.

Module 8Level 3internal force diagram

The horizontal struts of the tower

In the wind-loaded tower, the horizontal members tying the two legs together at each level (E and F) — what do they carry?

Predict first, then reveal

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

ACompression — they act as struts, holding the two legs apart as the diagonal bracing tries to pull them together under the wind shear.BTension, because horizontal members are ties.CZero force, because no vertical load acts on them.

Module 8Level 3internal force diagram

Verticals of a Howe truss

In a Howe truss under gravity, the diagonals are in compression. What, then, do the vertical posts carry — and how does that compare with a Pratt truss?

Predict first, then reveal

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

AThe verticals are in tension — with the diagonals pushing, the verticals must pull, the exact opposite of a Pratt truss where the verticals push and the diagonals pull.BThe verticals are also in compression, like the diagonals.CThe verticals carry no force at all.

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