Chartered Civil Engineer (ICE) Engineering Mechanics and Structural Design Syllabus

Give the design value of concrete compressive strength used in EC2 and the typical partial factor.

$$f_{cd} = \frac{\alpha_{cc} f_{ck}}{\gamma_c}$$ with $\gamma_c = 1.5$ and $\alpha_{cc}$ commonly taken as 0.85 (UK NA), where $f_{ck}$ is the characteristic cylinder strength.

Give the design value of reinforcement yield strength in EC2 and its partial factor.

$$f_{yd} = \frac{f_{yk}}{\gamma_s}$$ with $\gamma_s = 1.15$; for typical UK rebar $f_{yk} = 500\ \text{MPa}$ so $f_{yd} \approx 435\ \text{MPa}$.

State the EC2 ultimate bending moment capacity expression for a singly-reinforced rectangular section (lever arm form).

$$M = A_s f_{yd}\, z$$ where $z$ is the lever arm, $z = d\left(0.5 + \sqrt{0.25 - \frac{K}{1.134}}\right) \le 0.95d$ and $K = \dfrac{M}{b d^2 f_{ck}}$.

What is the EC2 variable strut inclination method used for, and what is the allowable range of $\theta$?

It designs shear reinforcement using a truss analogy with a concrete compression strut at angle $\theta$ to the horizontal. EC2 limits $1.0 \le \cot\theta \le 2.5$, i.e. $21.8^\circ \le \theta \le 45^\circ$.

Give the EC2 shear resistance provided by vertical links (shear reinforcement).

$$V_{Rd,s} = \frac{A_{sw}}{s}\, z\, f_{ywd}\cot\theta$$ where $A_{sw}/s$ is the link area per unit length, $z \approx 0.9d$ the lever arm, $f_{ywd}$ the link design yield strength.

What governs torsion design of concrete members in EC2, and what model is used?

Torsion is resisted using a thin-walled closed section (space truss) analogy: the section is idealised as an equivalent hollow box, with diagonal compression struts and closed links plus longitudinal bars resisting the torsional shear flow. Combined torsion+shear must satisfy interaction limits.

Why is minimum cover specified in concrete design, and what two requirements set it?

Cover protects reinforcement and ensures durability and fire resistance. EC2 sets $c_{nom} = c_{min} + \Delta c_{dev}$, where $c_{min}$ is the greater of bond requirement (bar diameter) and the durability (exposure class) requirement, and $\Delta c_{dev}$ (typically 10 mm) is an allowance for deviation.

What are EC2 exposure classes and give two examples.

Classifications of the environmental conditions affecting reinforcement corrosion that set minimum cover and concrete grade. Examples: X0 (no risk), XC (carbonation-induced corrosion), XD (chlorides not from sea), XS (chlorides from seawater), XF (freeze/thaw), XA (chemical attack).

How does EC2 control cracking for durability (two methods)?

By limiting crack width $w_k$ to a code limit (commonly 0.3 mm for typical reinforced concrete), achieved either by detailing rules — limiting bar diameter and bar spacing for a given stress — or by direct calculation of crack width.

What is the basic difference between a short and a slender concrete column in EC2?

A column is slender if its slenderness ratio $\lambda = l_0/i$ exceeds the limiting value $\lambda_{lim}$; slender columns must include second-order (buckling) effects, whereas short columns can be designed for the applied axial load and first-order moments only.

Define the effective length $l_0$ and slenderness ratio $\lambda$ of a column.

$l_0$ is the buckling length accounting for end restraints (e.g. $l_0 = 0.5L$ fixed-fixed, $L$ pinned-pinned, $2L$ cantilever). Slenderness $$\lambda = \frac{l_0}{i}, \qquad i = \sqrt{\frac{I}{A}}$$ where $i$ is the radius of gyration.

What is prestressed concrete and what are the two main methods of prestressing?

Concrete with internal compressive stresses introduced by tensioned tendons to counteract tensile stresses from service loads. Methods: pre-tensioning (tendons tensioned before casting) and post-tensioning (tendons stressed after the concrete hardens through ducts).

Name four sources of prestress loss in prestressed concrete.

Elastic shortening of concrete, creep of concrete, shrinkage of concrete, relaxation of the steel tendons; (in post-tensioning also friction/wobble losses and anchorage draw-in).

Write the elastic stress equation for a prestressed section under prestress force $P$ with eccentricity $e$ and moment $M$.

$$\sigma = \frac{P}{A} \pm \frac{P e\, y}{I} \mp \frac{M y}{I}$$ combining axial prestress, prestress moment $Pe$, and applied bending moment $M$ at fibre distance $y$.

Which Eurocode governs steel structures, and what is its number?

Eurocode 3 — BS EN 1993, 'Design of steel structures'.

State the EC3 design tension resistance of a member (gross and net section checks).

$$N_{t,Rd} = \min\left( \frac{A f_y}{\gamma_{M0}}, \; \frac{0.9 A_{net} f_u}{\gamma_{M2}} \right)$$ yielding of the gross section vs. ultimate failure of the net section through holes.

What are EC3 cross-section classes 1 to 4, and what do they govern?

Classification by local buckling of compression elements: Class 1 (plastic — can form a hinge with rotation), Class 2 (compact — reach $M_{pl}$ but limited rotation), Class 3 (semi-compact — reach $M_{el}$ only), Class 4 (slender — local buckling before yield, use effective section).

Give the EC3 design buckling resistance of a compression member.

$$N_{b,Rd} = \frac{\chi A f_y}{\gamma_{M1}}$$ where $\chi \le 1.0$ is the reduction factor for the relevant buckling mode, a function of the non-dimensional slenderness $\bar{\lambda}$ and buckling curve.

State the Euler critical buckling load for a pin-ended strut.

$$N_{cr} = \frac{\pi^2 E I}{L_{cr}^2}$$ where $L_{cr}$ is the effective (buckling) length. The non-dimensional slenderness is $\bar{\lambda} = \sqrt{A f_y / N_{cr}}$.

What is lateral torsional buckling (LTB) of a beam?

An instability in which an unrestrained beam in bending buckles sideways and twists out of plane before reaching its full in-plane moment capacity. It is governed by the buckling resistance moment $M_{b,Rd}$ in EC3.

Give the EC3 buckling resistance moment for lateral torsional buckling.

$$M_{b,Rd} = \chi_{LT}\, W_y\, \frac{f_y}{\gamma_{M1}}$$ where $\chi_{LT} \le 1.0$ is the LTB reduction factor (from $\bar{\lambda}_{LT}$ and the buckling curve) and $W_y$ is the appropriate section modulus.

Name two ways to prevent or reduce lateral torsional buckling in a steel beam.

Provide lateral restraint to the compression flange (reduce effective unrestrained length $L_{cr}$), or use a section with high lateral/torsional stiffness (e.g. higher $I_z$, closed/hollow sections).

List the failure modes that must be checked for a bolted connection in EC3.

Bolt shear, bolt bearing on the plate, plate tension/block tearing (block shear), bolt tension, and combined shear+tension. The connection capacity is the lowest of these.

Give the EC3 design shear resistance of a single bolt (one shear plane).

$$F_{v,Rd} = \frac{\alpha_v f_{ub} A}{\gamma_{M2}}$$ where $\alpha_v = 0.6$ (classes 4.6, 5.6, 8.8) or $0.5$ (10.9), $f_{ub}$ is the bolt ultimate strength and $A$ the shear area (gross or tensile).

What are the two principal types of welds, and how is fillet weld strength checked in EC3?

Fillet welds and butt (full/partial penetration) welds. Fillet welds are checked by the directional method on the throat using stress components: $$\sqrt{\sigma_\perp^2 + 3(\tau_\perp^2 + \tau_\parallel^2)} \le \frac{f_u}{\beta_w \gamma_{M2}}, \quad \sigma_\perp \le \frac{0.9 f_u}{\gamma_{M2}}$$

Which Eurocode covers steel-concrete composite structures and what is the key load-transfer component?

Eurocode 4 — BS EN 1994, 'Design of composite steel and concrete structures'. Shear connectors (typically headed studs) transfer longitudinal shear at the steel-concrete interface to achieve composite action.

Define full vs partial shear connection in a composite beam.

Full shear connection: enough shear connectors are provided to develop the full plastic moment of the composite section. Partial shear connection: fewer connectors are used, so the moment capacity is limited by the strength of the connection (degree of connection $\eta < 1$).

Which Eurocode defines actions (loads) on structures, and name its main parts.

Eurocode 1 — BS EN 1991, 'Actions on structures'. Parts cover densities/self-weight and imposed loads (1-1), fire actions, snow (1-3), wind (1-4), thermal, construction loads, accidental actions (1-7), and traffic loads on bridges (Part 2).

State the ULS fundamental load combination (EC0/EC1) for persistent design situations.

$$\sum \gamma_{G,j} G_{k,j} + \gamma_Q Q_{k,1} + \sum \gamma_{Q,i}\psi_{0,i} Q_{k,i}$$ Typical UK values: $\gamma_G = 1.35$ (unfavourable permanent), $\gamma_Q = 1.5$ (leading variable), with $\psi_0$ combination factors for accompanying variable actions.

What do the $\psi_0$, $\psi_1$ and $\psi_2$ combination factors represent in the Eurocodes?

$\psi_0$ = combination value (for accompanying actions in ULS), $\psi_1$ = frequent value (e.g. for frequent SLS/accidental leading), $\psi_2$ = quasi-permanent value (long-term/permanent proportion of a variable action).

Distinguish characteristic strength from design strength of a material.

Characteristic strength is a specified fractile of test results (usually the 5% lower fractile, e.g. $f_{ck}$, $f_{yk}$). Design strength is the characteristic value divided by a partial safety factor $\gamma_M$ (e.g. $f_{cd}=f_{ck}/\gamma_c$), accounting for material variability and modelling uncertainty.

Give typical values of Young's modulus for structural steel, concrete and timber.

Steel: $E \approx 210\ \text{GPa}$. Concrete (secant): $E_{cm} \approx 30\text{–}35\ \text{GPa}$ for normal grades. Timber (softwood, parallel to grain): $E_{0,mean} \approx 8\text{–}12\ \text{GPa}$.

Contrast the behaviour of concrete, steel, timber and masonry in tension and compression.

Concrete: strong in compression, weak in tension (needs reinforcement). Steel: strong and ductile in both tension and compression (isotropic). Timber: anisotropic, moderate strength along the grain, weak across the grain. Masonry: strong in compression, very weak in tension (designed to avoid tension).

Which Eurocode governs timber design, and what factor accounts for load duration and moisture?

Eurocode 5 — BS EN 1995. The modification factor $k_{mod}$ adjusts strength for load-duration class and service (moisture) class: $$f_d = \frac{k_{mod}\, f_k}{\gamma_M}$$

Which Eurocode governs masonry design, and what is the characteristic compressive strength expression?

Eurocode 6 — BS EN 1996. The characteristic compressive strength of masonry: $$f_k = K\, f_b^{\,\alpha}\, f_m^{\,\beta}$$ where $f_b$ is the unit strength, $f_m$ the mortar strength, and $K$, $\alpha$, $\beta$ are constants depending on masonry/mortar type.

Define structural robustness and disproportionate (progressive) collapse.

Robustness is the ability of a structure to withstand localised damage without collapse disproportionate to the original cause. Disproportionate collapse is the spread of failure from a local event (e.g. loss of one column) to a much larger portion of the structure.

What are the main strategies in EC1-7 (BS EN 1991-1-7) to ensure robustness against disproportionate collapse?

Provide horizontal and vertical ties; design key elements to resist an accidental design action (e.g. 34 kN/m²); allow notional removal of single members and check alternative load paths; and adopt appropriate detailing based on the building's consequence/risk class.

What are tie forces in robustness design and what do they provide?

Minimum specified tensile capacities required in horizontal (peripheral and internal) and vertical members so that, if an element is lost, the structure can develop catenary/alternative load paths and bridge over the damage, preventing progressive collapse.

What is the difference between Serviceability Limit State (SLS) and Ultimate Limit State (ULS)?

ULS concerns safety against collapse — strength, stability, overturning, rupture (uses factored loads). SLS concerns normal use and comfort — deflection, cracking, vibration, and durability (generally uses unfactored/characteristic or quasi-permanent loads).

For a simply supported beam under a central point load $P$, give the maximum bending moment and mid-span deflection.

$$M_{max} = \frac{PL}{4}, \qquad \delta_{max} = \frac{PL^3}{48EI}$$ at mid-span, where $L$ is the span and $EI$ the flexural rigidity.

For a simply supported beam under a uniformly distributed load $w$, give the maximum bending moment and shear.

$$M_{max} = \frac{wL^2}{8} \ \text{(mid-span)}, \qquad V_{max} = \frac{wL}{2}\ \text{(at supports)}$$ and the mid-span deflection $\delta_{max} = \dfrac{5wL^4}{384EI}$.