Practice

Revision sheets and timed examination practice

Open “Animation lab” beside a teaching step for a visual explanation or a walkthrough of its original expressions. Models are illustrative; source answers remain unchanged.

Chinese–English terminology

Use these sheets after learning the full methods. They compress decisions, not prerequisites. Both supplied papers make floor-beam design compulsory; the three optional families have equal $30$ -mark allocations. Practise every family and choose exam options from demonstrated performance, not predicted topics.

An outcome-based revision path

Session	What to do	Ready to advance when…
1 · foundations	Read units, algebra and equilibrium. Complete practiceP1–P5.	You can draw a free body, convert $cm$ properties and identify characteristic versus design loads.
2 · fully restrained beams	Work Chapter 3 examples 1/2, then Tutorial 3 Q2 and one compulsory past-paper question.	You transfer slab→B1→B2 loads without double factoring and select the correct deflection load.
3 · connections	Study all ten Chapter 2 examples, then complete Tutorial 2 with the hints closed.	You distinguish shear planes, bearing paths, net area, in-plane torsion and out-of-plane tension.
4 · unrestrained beams	Work Chapter 3 examples 3/4 and Tutorial 3 Q3–Q5.	You keep vertical spans separate from LTB segments and calculate their own quarter points.
5 · columns	Work all five Ch 4 examples and five tutorial questions.	You choose curves per axis and use the correct moments/denominators in three interaction checks.
6 · integrate	Complete both assignments and remaining past-paper parts. Review all companion notes and source discrepancies.	You can explain every assumption and missing-input limitation.
7 · independent transfer	Complete practiceStage 3, then the timed mock.	You solve a changed load/geometry case without referring to a completed solution.

Animation labFollow the calculation sequence1 concept

Supplement to the original lesson. Enable JavaScript to play, step through calculations and rotate 3D models. The following explanation remains readable offline.

Locate the load, supports, connection geometry and any stated assumptions.
Keep given values, table lookups and calculated values distinct; reconcile their units.
The calculation player steps through the existing expressions in their original order.
Compare demand with resistance or the relevant limit. Keep missing inputs and conditional conclusions explicit.

Revision sheet 1 · floor beams and local checks

Mark columns, actual vertical span and one-way slab direction. Interior tributary width is half the bay on each side; edges differ.
$G_{slab} = thickness (m) \times unit weight (\frac{kN}{m^{3}}) + finishes load$ $w_{G} = G_{slab} \times tributary width + self-weight$ $w_{Q} = Q \times tributary width$ $self-weight = \frac{mass per metre (\frac{kg}{m}) \times g}{1000}$
Use $1.4 G + 1.6 Q$ for the stated gravity combination. A transferred design reaction is already factored.
For simple UDL: $R = \frac{w L}{2}$ , $M_{\max} = \frac{w L^{2}}{8}$ . For centralP addP/2 andPL/4. For off-centre/multiple loads use moment equilibrium and piecewiseV/ $M$ .
Read actual section row. Choosepy byT; $ε = \sqrt{\frac{275}{p_{y}}}$ ; check flange/web class.
$V_{c} = \frac{p_{y} A_{v}}{\sqrt{3}}$ . For rolled major-axis shearAv=tD. IfV≤0.6Vc, Class 1/2Mc=min(pyS,1.2pyZ). Otherwise use high-shear reduction.
If required, bearingPbw=(b 1+nk)tpyw withcorrect end/internaln; web buckling uses the appropriate end-distance and restraint branch. Missing contact data means an incomplete local check.
For imposed-only SLS use unfactoredQ: $δ_{UDL} = \frac{5 w L^{4}}{384 E I}$ , $δ_{centralP} = \frac{P L^{3}}{48 E I}$ . Add compatible elastic contributions. Compare to the specified finish/function limit.

Quick unit check: $w$ is measured in $\frac{kN}{m}$ or $\frac{N}{mm}$ has the same numerical value in these units; $P$ converts from $kN$ to $N$ by $1000$ ; $I$ converts from ${cm}^{4}$ to ${mm}^{4}$ by $10000$ . Do not use the midspan point-load formula for a load away from midspan.

Full reference example · Compulsory exam application

Animation labFollow the floor load in 3D14 concepts · 10 source expressions

Supplement to the original lesson. Enable JavaScript to play, step through calculations and rotate 3D models. The following explanation remains readable offline.

The floor carries pressure in $\frac{kN}{m ^{2}}$ . The highlighted strip belongs to one secondary beam.
Multiply pressure by tributary width: $w = q \times b$ . The illustration uses $q = 5 \frac{kN}{m ^{2}}$ .
A primary beam receives the secondary beam reaction at their connection, not a new full-span UDL.
Trace reactions down to columns and foundations. Count each loaded area once.

Revision sheet 2 · LTB decisions

Identify which flange is compressed and all effective lateral/torsional restraints. Mark the load-height condition.
DeriveLE from the actual applicable restraint condition; the vertical support span and unrestrained length may differ.
Each segment: $λ = \frac{L_{E}}{r_{y}}$ ; $v = {[1 + 0.05 {(\frac{λ}{x})}^{2}]}^{- \frac{1}{4}}$ ; $λ_{LT} = u v λ \sqrt{β_{W}}$ . Once Class 1/2 is established, $β_{W} = 1$ .
Read Table 8.3a atλLT and correctpy, interpolate; $M_{b} = p_{b} S_{x}$ . Keep $N \cdot mm$ andkNm conversions explicit.
GetmLT from a matching standard moment diagram or the general absolute quarter-point expression. Use the current segment’s quarters.
CheckmLT Mmax≤Mb for each potentially governing segment. Separately retain actualMmax≤Mc andV≤Vc.
Adding a lateral restraint changes stability length, not the verticalBMD, unless it is also a new vertical support.

General expression:

m_{LT} = \max [0.44, 0.2 + \frac{0.15 | M_{2} | + 0.5 | M_{3} | + 0.15 | M_{4} |}{M_{\max}}]

End-couple variant · Unequal segment loads

Animation labA beam bends sideways and twists4 concepts · 6 source expressions

Supplement to the original lesson. Enable JavaScript to play, step through calculations and rotate 3D models. The following explanation remains readable offline.

For the illustrated sagging beam the top flange is compressed.
The unrestrained compression flange can move sideways while the complete cross-section twists.
Only effective restraints divide the member into unbraced segments. They do not automatically add vertical supports.
Use the segment effective length, section properties and matching moment factor. This is an exaggerated mode shape, not a calculated displacement.

Revision sheet 3 · bolts and plates

Sketch ONE transfer half for a splice; identify plates and bolt shear planes. For a concentric group divide force by number of parallel bolts.
BoltPs=psAs per plane; $P_{t} = A_{t} p_{t}$ ; $P_{nom} = 0.8 A_{t} p_{t}$ . Use threads/shank area appropriately.
Bolt bearingPbb=dtp pbb. With two covers compare central contact with sum of outer contacts.
For each connected part compare diameter bearing, $k_{bs} d t p_{bs}$ ; end bearing, $0.5 k_{bs} e t p_{bs}$ ; andmin(1.5lc tUs,2dtUb). Use net hole ligamentlc and correct load share.
For tension follow candidate hole paths andKe cap. Apply single/double bolted-angle reduction $0.5 a_{2}$ / $0.25 a_{2}$ as appropriate.
In-plane eccentricity: $F_{s} = \frac{P}{n}$ ; torsional vector components follow from $M = P e$ and $J = Σ (x^{2} + y^{2})$ . Add components in the same direction before finding the resultant.
For out-of-plane bracket tension: $F_{t, \max} = \frac{P e y_{\max}}{Σ y^{2}}$ about the course pivot. Check applicable prying assumptions. $\frac{F_{s}}{P_{s}} + \frac{F_{t}}{P_{nom}} \leq 1.4$ and individualchecks.
Check hole clearance,pitch,gauge,end/edge distances and any requested block shear or long-joint/grip adjustment. Do not equate bolt shear adequacy with whole-joint adequacy.

Full formulas and applicability · Every tabulated cell worked

Animation labSeparate the block-shear paths10 concepts · 7 source expressions

Supplement to the original lesson. Enable JavaScript to play, step through calculations and rotate 3D models. The following explanation remains readable offline.

A block containing the connection can detach from the surrounding plate.
The paths parallel to the applied force carry shear.
The closing path across the end of the block carries tension.
Use the specified gross/net deductions and resistance expression. This is different from a single straight net-section fracture.

Revision sheet 4 · welds

Identify the steel/electrode pairing. $90 °$ fillet weld uses $a = 0.7 s$ ， $q_{cap} = \frac{0.7 s p_{w}}{1000} \frac{kN}{mm}$ .
Direct concentric force: effective length= $\frac{P}{q_{cap}}$ distributed among actual parallel runs. Physical terminated run=effective+ $2 s$ .
For unequal angles balance forces about the section centroid using table coordinates; unequal side distances require unequal load shares.
For in-plane eccentric group, locate line centroid, calculateJline[ ${mm}^{3}$ ], and useqdirect=P/L plus torsional componentsMx/J andMy/J. Add vectors at candidate corners.
For out-of-plane flange/web model use its stated rotation axis and force couple; do not apply a centroidal in-plane formula blindly.
Round size/length UP; then check thicker-part minimumleg, thinner-edge maximumleg, minimum effective length, lap, returns and transverse-spacing rule.
Check parent-metal/angle/cover capacities where requested. If minleg>maxleg, redesign the detail; do not select an impossible compromise.

Rectangular group · A detailing conflict · Corrected splice

Animation labFrom fillet leg to effective throat6 concepts · 2 source expressions

Supplement to the original lesson. Enable JavaScript to play, step through calculations and rotate 3D models. The following explanation remains readable offline.

An equal-leg fillet between perpendicular plates has an approximately right-triangular section.
For this geometry, throat $a \approx 0.7 s$ . It is shorter than the leg.
Effective resisting area = $a \times L_{eff}$ . With $p_{w} = 220 \frac{N}{mm ^{2}}$ here, capacity per length is $0.7 s \times 220 \frac{N}{mm}$ .
Use the course end allowances, minimum size and length rules; increasing the geometric length alone does not resolve every detailing check.

Revision sheet 5 · columns with bending

Classify frame/model and end restraints; calculateLEx, $L_{Ey}$ . In simple construction first derive reactions,eccentricities and stiffness sharing.
Read exact UC row andpy bythickness. Classify under combined compression/bending, not a pure-bending web assumption.
Section check usesAgpy and prescribed capped sectionMc with amplified moments.
For each axisλ=LE/r; choose curve from type/thickness/axis; interpolatepc; $P_{cx} = A_{g} p_{cx}$ , $P_{cy} = A_{g} p_{cy}$ ,Pc=min.
Flexural member equation uses elasticpyZ denominators and the lecture’s amplified moments withmx, $m_{y}$ .
LTB equation usesPcy, the prescribed amplifiedMLT, $M_{b}$ and FIRST-ORDER minor-axisMy in the course Eq.8.81. Do not amplifyMLT twice.
For simple construction, use the stated $m = 1$ rule and $λ_{LT} = \frac{0.5 L}{r_{y}}$ , where $L$ is actual storey height. Continuous/non-sway examples instead use $u$ , $v$ .
All three requested interaction results must pass. State the governing one and any model assumptions.

End-moment worked example · Simple-construction example

Animation labA strong slice can belong to an unstable member11 concepts · 4 source expressions

Supplement to the original lesson. Enable JavaScript to play, step through calculations and rotate 3D models. The following explanation remains readable offline.

Combine axial compression and the two bending demands using the specified section resistances.
The whole member adds effective-length and buckling-curve effects.
This uses its own moment factor and bending resistance; it is not a copy of the section check.
Elastic, plastic and buckling resistances are not interchangeable. Read the three original expressions and their first-order/amplified moments.

Revision sheet 6 · short theory that earns marks

Prompt	A concise explanatory answer
ULS versus SLS	ULS prevents strength/stability failure;SLS limits unacceptable deformation/vibration under the stated service actions.
Corrosion protection	Paint isolates steel from moisture/oxygen; galvanizing uses a zinc barrier plus sacrificial protection.
Fire protection	Solid casing,hollow casing andprofile casing reduce steel heating; draw the steel outline and protective layer. Do not invent a rating or thickness.
Four rolled shapes	Sketch and label UB,UC,channel,angle; showweb/flanges/legs distinctly.
First versussecond order	First order equilibrates loads on the original geometry; second order includes additional effects from displaced geometry under axial load.
Why section class matters	Local plate buckling limits available plasticity;class selects plastic,elastic or effective section resistance.
Why LTB can govern	The compression flange can move laterally and the beam twist despite adequate local bending/shear strength.
Why bolts andplates need checks	The joint can fail in a fastener or in the surrounding connected metal; the force must survive every transfer stage.

Animation labTwo different design questions10 concepts

Supplement to the original lesson. Enable JavaScript to play, step through calculations and rotate 3D models. The following explanation remains readable offline.

ULS compares factored actions with the applicable resistance to yielding, rupture or instability.
SLS checks movement, vibration or another specified use requirement.
A beam can be strong enough but deflect too much. The two checks need their own loads and denominators.
A resistance pass cannot stand in for a serviceability pass. Complete all requested checks.

Sit the 120-minute mock

Open the questions-only mock. Use a separate timer; record start/finish on paper. Keep answers closed and choose two options before the end of the reading period. All questions and marking suggestions are explicitly invented.

After marking, record first wrong decisions in the error log. Repeat only after solving a changed question independently. A high score obtained while copying a solution is not evidence that you can handle an unfamiliar variant.

Animation labFollow the calculation sequence1 concept

Supplement to the original lesson. Enable JavaScript to play, step through calculations and rotate 3D models. The following explanation remains readable offline.

Locate the load, supports, connection geometry and any stated assumptions.
Keep given values, table lookups and calculated values distinct; reconcile their units.
The calculation player steps through the existing expressions in their original order.
Compare demand with resistance or the relevant limit. Keep missing inputs and conditional conclusions explicit.