How do you find the support reactions of a simply supported beam?

Apply the two equations of static equilibrium. Replace any uniformly distributed load with a single resultant force at the centre of the loaded length, then take moments about one support so its reaction drops out of the equation. Solve for the far reaction, then use the sum of vertical forces equals zero to find the first reaction. Always quote both reactions with units (N or kN).

What is the difference between stress and strain?

Stress is force per unit cross-sectional area, sigma equals F over A, measured in pascals (Pa) or megapascals (MPa). Strain is the fractional change in length, epsilon equals change in length over original length, and it is dimensionless. Young's modulus links the two in the elastic region: E equals stress over strain, so a stiff material like steel (E around 200 GPa) strains very little for a given stress.

How does the method of joints work for a pin-jointed truss?

First find the support reactions for the whole truss using overall equilibrium. Then move to a joint with at most two unknown member forces and apply sum of horizontal forces equals zero and sum of vertical forces equals zero at that joint. Assume each unknown member is in tension; a negative answer means the member is actually in compression. Work joint to joint until every member force is known.

Why is concrete reinforced with steel?

Concrete is strong in compression (a typical structural grade carries about 32 MPa) but weak in tension (only about 3 MPa), so it cracks wherever bending creates tensile stress. Steel is strong in both tension and compression, so reinforcing bars are placed in the tensile zone of a member to carry the tensile force while the concrete carries the compression. The two materials bond well and expand at similar rates with temperature.

What grades of structural steel does the HSC expect?

Australian practice uses grade 250 (yield stress 250 MPa) for standard mild structural steel and grade 350 (yield stress 350 MPa) where higher capacity at lower mass is needed. Because axial capacity scales with yield stress, grade 350 carries about 40 percent more load than grade 250 at the same cross-section, at the cost of higher price and slightly lower ductility.

← Engineering Studies guides

NSWEngineering Studies

HSC Engineering Studies Civil Structures: deep-dive 2026 guide

Deep-dive on the HSC Engineering Studies Civil Structures module. Equilibrium of beams and trusses, support reactions, the method of joints, stress, strain, Young's modulus, structural steel grades and reinforced concrete, with worked calculations and exam-style questions.

Generated by Claude Opus 4.717 min readNESA-ENG-CIVILUpdated 2026-05-24

Jump to a section

How Civil Structures fits into HSC Engineering Studies
Static equilibrium: the foundation
Support reactions on a simply supported beam
Pin-jointed trusses and the method of joints
Stress, strain and Young's modulus
Reading stress-strain curves
Selecting structural materials
Common Civil Structures examiner traps
Check your knowledge

How Civil Structures fits into HSC Engineering Studies

Civil Structures is the module where the statics and materials science of the course come together. You analyse the forces inside beams, trusses and frames, then you ask whether the materials chosen can carry those forces safely. Almost every Section II calculation in this module reduces to one of two ideas: equilibrium (the structure is not accelerating, so forces and moments balance) and the stress-strain relationship (loads create internal stresses, and materials respond with strain up to a limit).

NESA examines this module quantitatively. You are expected to draw a free-body diagram, set out equilibrium equations explicitly, and carry consistent units through to a final answer with the correct sign and magnitude. The Australian context (the Sydney Harbour Bridge, the Snowy Mountains Scheme, BlueScope steel from Port Kembla) gives you the named examples markers reward.

Static equilibrium: the foundation

A civil structure that is standing still has zero net force and zero net moment. In two dimensions this gives three independent equations:

These three equations let you solve for up to three unknown reactions on a statically determinate structure. For a simply supported beam (a pin at one end, a roller at the other) there are exactly the right number of unknowns, which is why the HSC sticks to determinate cases.

A uniformly distributed load (UDL) of intensity $w$ (in N/m or kN/m) over a length $L$ is replaced for calculation purposes by a single resultant force of magnitude $wL$ acting at the centre of the loaded length. This single trick handles most distributed-load questions.

Support reactions on a simply supported beam

The standard method:

Draw the free-body diagram. Mark all applied loads and the unknown reactions.
Replace each UDL with its resultant at the centre of the loaded span.
Take moments about one support. That support's reaction has zero moment arm and drops out, leaving one equation in one unknown.
Solve for the far reaction.
Apply $\sum F_y = 0$ to find the near reaction.

Worked example: beam with a point load and a UDL

A simply supported beam spans 6.0 m. It carries a point load of 12 kN located 2.0 m from the left support, plus a UDL of 4 kN/m over the full 6.0 m span. Find the left reaction $R_L$ and the right reaction $R_R$ .

Step 1: resolve the UDL. Total UDL force is $w L = 4 \times 6 = 24$ kN, acting at midspan, $3.0$ m from the left support.

Step 2: moments about the left support (take clockwise positive):

\sum M_L = 0 = (12)(2.0) + (24)(3.0) - R_R(6.0)

R_R = \frac{(12)(2.0) + (24)(3.0)}{6.0} = \frac{24 + 72}{6.0} = 16 \text{ kN}

Step 3: vertical equilibrium.

R_L + R_R = 12 + 24 = 36 \text{ kN}

R_L = 36 - 16 = 20 \text{ kN}

The left support carries 20 kN, the right support carries 16 kN. Check: moments about the right support give $R_L(6) = 12(4) + 24(3) = 48 + 72 = 120$ , so $R_L = 20$ kN. Consistent.

Pin-jointed trusses and the method of joints

A truss is an assembly of straight members joined at pins. Because the joints are pins and loads act only at the joints, every member carries pure axial force: either tension (pulling away from each joint) or compression (pushing into each joint). No member carries bending.

The method of joints applies equilibrium at one joint at a time:

The procedure: first find the support reactions using overall equilibrium, then start at a joint with at most two unknown members. Assume both unknowns are in tension (drawn pointing away from the joint). A positive answer confirms tension; a negative answer means the member is in compression.

Worked example: force in a truss member

A symmetric triangular truss has a horizontal bottom chord 8.0 m long between supports $A$ (left, pin) and $C$ (right, roller). The apex $B$ is 3.0 m above the midpoint of $AC$ . A single vertical load of 20 kN acts downward at the apex $B$ . Find the force in member $AB$ and state whether it is in tension or compression.

Reactions. By symmetry, each support carries half the load:

R_A = R_C = \frac{20}{2} = 10 \text{ kN upward}

Geometry of member $AB$ . It runs from $A$ (0, 0) to $B$ (4.0, 3.0), so its length is

L_{AB} = \sqrt{4.0^2 + 3.0^2} = \sqrt{16 + 9} = 5.0 \text{ m}

The member makes an angle with the horizontal whose sine is $3.0/5.0 = 0.6$ and cosine is $4.0/5.0 = 0.8$ .

Joint $A$ . Two unknown members meet here: $AB$ (sloping up to the right) and $AC$ (horizontal). Assume both in tension. Vertical equilibrium at $A$ :

\sum F_y = 0 = R_A + F_{AB}\sin\theta = 10 + F_{AB}(0.6)

F_{AB} = \frac{-10}{0.6} = -16.7 \text{ kN}

The negative sign means member $AB$ is in compression, carrying 16.7 kN. This makes physical sense: the sloping members of a loaded triangular truss push back against the downward apex load, so they are compression members, while the bottom chord is pulled apart in tension.

Stress, strain and Young's modulus

Once you know the internal forces, you check whether the material can carry them. Three definitions sit behind every materials calculation.

Typical Young's modulus values to commit to memory: structural steel $E \approx 200$ GPa, aluminium alloys $E \approx 70$ GPa, concrete $E \approx 25$ to $35$ GPa, and timber $E \approx 10$ GPa.

Worked example: stress, strain and extension

A steel tie bar has cross-sectional area $A = 250 \text{ mm}^2$ and original length $L = 2.0$ m. It carries a tensile load of $F = 50$ kN. Take $E = 200$ GPa for the steel. Find the stress, strain and extension.

Convert units. $A = 250 \text{ mm}^2 = 250 \times 10^{-6} \text{ m}^2$ , and $E = 200 \times 10^9$ Pa.

Stress.

\sigma = \frac{F}{A} = \frac{50 \times 10^3}{250 \times 10^{-6}} = 2.0 \times 10^8 \text{ Pa} = 200 \text{ MPa}

Strain.

\varepsilon = \frac{\sigma}{E} = \frac{2.0 \times 10^8}{200 \times 10^9} = 1.0 \times 10^{-3}

Extension.

\Delta L = \varepsilon L = 1.0 \times 10^{-3} \times 2.0 = 2.0 \times 10^{-3} \text{ m} = 2.0 \text{ mm}

The working stress of 200 MPa sits just below the yield stress of grade 250 structural steel (250 MPa). For a safe design you would lower the load or increase the area to bring the stress comfortably below yield.

Reading stress-strain curves

Ductile materials such as mild steel show a straight elastic region up to the yield point, then a yield plateau, then strain hardening up to the ultimate tensile strength, then necking and fracture. Grade 250 structural steel has yield stress around 250 MPa and ultimate tensile strength around 410 MPa. Ductile materials give visible warning (large plastic deformation) before they fail.

Brittle materials such as cast iron, glass and concrete in tension show an almost straight line with little or no plastic region, then sudden fracture. The area under the stress-strain curve represents the energy absorbed per unit volume before failure (toughness); ductile materials are tough, brittle materials are not.

Selecting structural materials

Structural steel comes in grades named by yield stress in MPa. The common Australian grades are 250 ( $f_y = 250$ MPa, $f_u = 410$ MPa) and 350 ( $f_y = 350$ MPa, $f_u = 480$ MPa). Standard sections include universal beams (UB, deep, optimised for bending), universal columns (UC, roughly square, optimised for axial compression), channels, angles and hollow sections. Members are joined by bolts (property class 4.6 or 8.8) or welds, and designed to Australian Standard AS4100.

Worked example: axial capacity of a steel column

A 200UC59.5 universal column has a cross-sectional area of $7600 \text{ mm}^2$ . Compare the axial load at which the steel reaches yield for grade 250 and grade 350.

For grade 250:

F = f_y A = 250 \text{ N/mm}^2 \times 7600 \text{ mm}^2 = 1.9 \times 10^6 \text{ N} = 1900 \text{ kN}

For grade 350:

F = 350 \times 7600 = 2.66 \times 10^6 \text{ N} = 2660 \text{ kN}

The grade 350 section carries $2660 / 1900 = 1.40$ , that is 40 percent more load for the same steel mass. (Working in N/mm $^2$ and mm $^2$ keeps the answer in newtons directly, since $1 \text{ MPa} = 1 \text{ N/mm}^2$ .)

Reinforced and pre-stressed concrete exploits the fact that concrete is strong in compression (about 32 MPa for a grade N32 mix) but weak in tension (about 3 MPa). Reinforced concrete places passive deformed steel bars in the tensile zone of a member so the steel carries tension while the concrete carries compression. Pre-stressed concrete goes further: high-tensile tendons are tensioned (pre-tensioned before the pour, or post-tensioned after curing) so the concrete is held in permanent compression, cancelling tensile stresses before service load even arrives. The Snowy Mountains Scheme and most Australian motorway bridges rely on pre-stressed concrete girders.

Common Civil Structures examiner traps

Treating a UDL as a point load at its end instead of a resultant at the centre of the loaded length.
Mixing units: forgetting that $1 \text{ MPa} = 1 \text{ N/mm}^2$ , or that area in $\text{mm}^2$ must be converted to $\text{m}^2$ (divide by $10^6$ ) when the load is in newtons and you want pascals.
Using diameter instead of radius, or forgetting $A = \pi d^2 / 4$ for a circular bar.
Forgetting the sign convention for truss members: positive equals tension, negative equals compression.
Reading Young's modulus from the wrong part of the stress-strain curve. $E$ is the slope of the initial elastic region only.

Check your knowledge

Work through these under exam conditions, then check against the solutions block. Show a free-body diagram for every statics question and carry units on every line.

State the two (in 2D, three) equations of static equilibrium and explain why taking moments about a support is a useful first step when finding beam reactions. (3 marks)
A simply supported beam spans 8.0 m. It carries point loads of 15 kN at 2.0 m from the left support and 25 kN at 6.0 m from the left support. Calculate the left and right support reactions. (4 marks)
A simply supported beam spans 5.0 m and carries a UDL of 6.0 kN/m over its full length plus a central point load of 20 kN at midspan. Calculate both support reactions. (4 marks)
Define stress, strain and Young's modulus, giving the units of each. (3 marks)
An aluminium strut of cross-sectional area $400 \text{ mm}^2$ and length $1.5$ m carries an axial compressive load of 28 kN. Young's modulus for the aluminium is 70 GPa. Calculate (a) the compressive stress, (b) the strain, and (c) the change in length. (5 marks)
A circular steel rod of diameter 20 mm and length 3.0 m carries a tensile load of 60 kN. Take $E = 200$ GPa. Calculate (a) the cross-sectional area, (b) the stress, and (c) the extension. State whether the stress is below the grade 250 yield of 250 MPa. (5 marks)
A symmetric triangular truss has a horizontal bottom chord $AC$ of length 6.0 m between a pin support at $A$ and a roller support at $C$ . The apex $B$ is 4.0 m vertically above the midpoint of $AC$ . A vertical downward load of 30 kN acts at $B$ . Calculate the force in member $AB$ and state whether it is in tension or compression. (5 marks)
Compare reinforced concrete and pre-stressed concrete. Identify the role of the steel in each, and name one Australian application of pre-stressed concrete. (4 marks)

Solutions

Q1: The equations of static equilibrium are $\sum F_x = 0$ , $\sum F_y = 0$ and $\sum M = 0$ (in two dimensions). They state that a body that is not accelerating has zero net force and zero net moment. Taking moments about a support is useful because that support's reaction passes through the moment centre and so has zero moment arm; it drops out of the moment equation, leaving a single equation in the single unknown of the other reaction.
Q2: Moments about the left support (clockwise positive):
$\sum M_L = 0 = (15)(2.0) + (25)(6.0) - R_R(8.0)$

$R_R = \frac{30 + 150}{8.0} = \frac{180}{8.0} = 22.5 \text{ kN}$

Vertical equilibrium: $R_L + R_R = 15 + 25 = 40$ kN, so $R_L = 40 - 22.5 = 17.5$ kN. Left reaction 17.5 kN, right reaction 22.5 kN.
Q3: UDL resultant: $w L = 6.0 \times 5.0 = 30$ kN at midspan (2.5 m). The 20 kN point load is also at midspan. By symmetry both loads act at the centre, so each support carries half of the total load. Total load $= 30 + 20 = 50$ kN, so $R_L = R_R = 25$ kN. (Check by moments about the left support: $\sum M_L = 30(2.5) + 20(2.5) - R_R(5.0) = 75 + 50 - 5R_R = 0$ , giving $R_R = 25$ kN.)
Q4: Stress is force per unit cross-sectional area, $\sigma = F/A$ , units pascals (Pa) or megapascals (MPa). Strain is the fractional change in length, $\varepsilon = \Delta L / L$ , dimensionless (no units). Young's modulus is the elastic-region slope of stress over strain, $E = \sigma / \varepsilon$ , units pascals or gigapascals (GPa).
Q5: $A = 400 \text{ mm}^2 = 400 \times 10^{-6} \text{ m}^2$ , $E = 70 \times 10^9$ Pa. (a) $\sigma = F/A = 28 \times 10^3 / (400 \times 10^{-6}) = 7.0 \times 10^7 \text{ Pa} = 70$ MPa. (b) $\varepsilon = \sigma / E = 7.0 \times 10^7 / 70 \times 10^9 = 1.0 \times 10^{-3}$ . (c) $\Delta L = \varepsilon L = 1.0 \times 10^{-3} \times 1.5 = 1.5 \times 10^{-3} \text{ m} = 1.5$ mm of shortening (compression).
Q6: (a) $A = \pi d^2 / 4 = \pi (0.020)^2 / 4 = \pi (4.0 \times 10^{-4}) / 4 = 3.14 \times 10^{-4} \text{ m}^2$ (or $314 \text{ mm}^2$ ). (b) $\sigma = F/A = 60 \times 10^3 / (3.14 \times 10^{-4}) = 1.91 \times 10^8 \text{ Pa} = 191$ MPa. (c) $\varepsilon = \sigma / E = 1.91 \times 10^8 / 200 \times 10^9 = 9.55 \times 10^{-4}$ , so $\Delta L = 9.55 \times 10^{-4} \times 3.0 = 2.87 \times 10^{-3} \text{ m} = 2.9$ mm. The stress of 191 MPa is below the grade 250 yield of 250 MPa, so the rod remains elastic.
Q7: Reactions: by symmetry $R_A = R_C = 30/2 = 15$ kN upward. Geometry of $AB$ : from $A$ (0, 0) to $B$ (3.0, 4.0), length $= \sqrt{3.0^2 + 4.0^2} = 5.0$ m, with $\sin\theta = 4.0/5.0 = 0.8$ and $\cos\theta = 3.0/5.0 = 0.6$ . At joint $A$ , assume $AB$ in tension. Vertical equilibrium: $\sum F_y = 0 = R_A + F_{AB}\sin\theta = 15 + F_{AB}(0.8)$ , so $F_{AB} = -15/0.8 = -18.75$ kN. The negative sign means $AB$ is in compression, carrying 18.75 kN.
Q8: In reinforced concrete the steel is passive deformed reinforcing bar placed in the tensile zone of a member; the steel carries the tensile stresses while the concrete carries compression. In pre-stressed concrete the steel is high-tensile tendons that are actively tensioned (pre-tensioned before the pour or post-tensioned after curing) so they place the concrete in permanent compression, cancelling service tensile stresses before they can crack the concrete. An Australian application of pre-stressed concrete: pre-stressed bridge girders on the Pacific Motorway (or the Sydney Harbour Tunnel approach spans, or post-tensioned structures in Snowy Hydro 2.0).