PE Civil — Structural Formula Sheet: Key Equations by Topic

Gravity Loads & Load Paths
9% of the exam

Dead, live, and construction loads; tributary areas and vertical and lateral load paths; live-load reduction; earth pressure and surcharge; and ASCE 7 strength and allowable-stress load combinations.

ASCE 7 Load Combinations (LRFD & ASD)

The ASCE 7-16 strength (LRFD) and allowable-stress (ASD) load combinations, how to find the one that governs a member, and the 1.0W wind factor.

LRFD basic gravity combination: $U = 1.2D + 1.6L + 0.5(L_r\ \text{or}\ S\ \text{or}\ R)$; ASCE 7-16 Eq. 2.3-2; governs most floor members. $D$=dead, $L$=live, $L_r$=roof live, $S$=snow, $R$=rain (all service-level nominal loads).
LRFD dead-only combination: $U = 1.4D$; ASCE 7-16 Eq. 2.3-1; controls only when dead load dominates (roughly $D > 8L$).
LRFD roof-load-led combination: $U = 1.2D + 1.6(L_r\ \text{or}\ S\ \text{or}\ R) + (L\ \text{or}\ 0.5W)$; ASCE 7-16 Eq. 2.3-3; lead action is roof live, snow, or rain. Companion $L$ may reduce to $0.5L$ where permitted.
LRFD wind combination: $U = 1.2D + 1.0W + L + 0.5(L_r\ \text{or}\ S\ \text{or}\ R)$; ASCE 7-16 Eq. 2.3-4. Wind factor is $1.0$ because 7-16 $W$ is strength-level. $L$ may reduce to $0.5L$ where $L_0\le100$ psf and not assembly.
LRFD uplift/overturning combination: $U = 0.9D + 1.0W$; ASCE 7-16 §2.3.1 combination (5); minimum dead resisting maximum wind — governs net uplift and anchor/connection tension.
ASD service combination with live: $\textstyle\sum = D + L$; ASCE 7-16 Eq. 2.4-2; basic gravity service combination compared to $R_n/\Omega$.
ASD combined live + roof: $\textstyle\sum = D + 0.75L + 0.75(L_r\ \text{or}\ S\ \text{or}\ R)$; ASCE 7-16 Eq. 2.4-4; the $0.75$ accounts for non-coincident transient maxima.
ASD wind combination: $\textstyle\sum = D + 0.6W$; ASCE 7-16 Eq. 2.4-5; $0.6W$ converts the strength-level map back to a service-level wind effect.
ASD combined live + wind + roof: $\textstyle\sum = D + 0.75L + 0.75(0.6W) + 0.75(L_r\ \text{or}\ S\ \text{or}\ R)$; ASCE 7-16 Eq. 2.4-6; companion-factored gravity plus reduced wind.
ASD uplift combination: $\textstyle\sum = 0.6D + 0.6W$; ASCE 7-16 Eq. 2.4-7 (§2.4.1 combination 7); $0.6D$ (not $1.0D$) resists overturning/uplift conservatively. Combination 8 in §2.4.1 is the seismic uplift $0.6D+0.7E$, not this wind case.

Where it lives: ASCE/SEI 7-16, Minimum Design Loads and Associated Criteria for Buildings and Other Structures — §2.3 (Strength Design / LRFD) and §2.4 (Allowable Stress Design) · ASCE/SEI 7-16 — Commentary C2 (basis of the strength-level wind map and the 1.0W / 0.6W factors) · AISC 360-16 / Steel Construction Manual, 15th ed. — application of LRFD ($\phi$) and ASD ($\Omega$) with the ASCE 7 combinations

Read the Gravity Loads & Load Paths chapter

Wind, Seismic & Environmental Loads
8% of the exam

Wind pressures and forces, seismic base shear and vertical distribution of lateral force, snow, rain, and ice loads, impact and moving (vehicular and crane) loads, and their delivery to the lateral system.

Seismic Base Shear (Equivalent Lateral Force)

The ASCE 7-16 equivalent lateral force base shear V = Cs·W, the seismic response coefficient and its caps, the approximate period, and how SDS, SD1, R and Ie set the demand.

Seismic base shear: $V = C_s\,W$; $V$ = total design base shear (kip), $C_s$ = seismic response coefficient (dimensionless), $W$ = effective seismic weight (kip) per ASCE 7-16 §12.7.2.
Seismic response coefficient (base form): $C_s = \dfrac{S_{DS}}{R/I_e}$; Short-period (constant-acceleration) value. $S_{DS}$ = design short-period spectral accel (g), $R$ = response modification factor, $I_e$ = importance factor.
Upper limit, T ≤ TL: $C_{s,\max} = \dfrac{S_{D1}}{T\,(R/I_e)}$; Velocity-region cap; governs for most moderate-to-long-period buildings. $S_{D1}$ = design 1-second spectral accel (g), $T$ = fundamental period (s).
Upper limit, T > TL: $C_{s,\max} = \dfrac{S_{D1}\,T_L}{T^2\,(R/I_e)}$; Long-period (displacement-region) cap beyond the corner period $T_L$ (s, mapped).
Lower limit (general): $C_{s,\min} = 0.044\,S_{DS}\,I_e \ge 0.01$; Floor on $C_s$ for all buildings; the result may not fall below this regardless of $T$ or $R$.
Lower limit (high seismicity): $C_{s,\min} = \dfrac{0.5\,S_1}{R/I_e}$; Additional floor where $S_1 \ge 0.6g$ (near-fault). $S_1$ = mapped 1-s MCE accel (g).
Approximate fundamental period: $T_a = C_t\,h_n^{\,x}$; $h_n$ = structural height (ft). Steel MF $C_t{=}0.028,x{=}0.8$; concrete MF $0.016,0.9$; EBF/BRBF $0.03,0.75$; other $0.02,0.75$.
Design spectral accelerations: $S_{DS} = \tfrac{2}{3}F_a S_S, \quad S_{D1} = \tfrac{2}{3}F_v S_1$; From mapped $S_S$, $S_1$ and site coefficients $F_a$, $F_v$; the $\tfrac{2}{3}$ scales MCE to design basis.
Computed-period upper bound: $T \le C_u\,T_a$; A rationally computed period may be used for the cap only up to $C_u T_a$ ($C_u$ from ASCE 7-16 Table 12.8-1, ~1.4–1.7).

Where it lives: ASCE/SEI 7-16, Minimum Design Loads and Associated Criteria for Buildings and Other Structures — §12.8 Equivalent Lateral Force Procedure · ASCE/SEI 7-16 — §11.4 Seismic Ground Motion Values (SDS, SD1, Fa, Fv) and §12.7.2 Effective Seismic Weight · ASCE/SEI 7-16 — Tables 12.2-1 (R, Cd, Ω0) and 12.8-1, 12.8-2 (Cu, Ct, x)

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Structural Analysis
13% of the exam

Reactions and determinacy, shear and moment diagrams, axial force, internal forces in beams and frames, combined normal and shear stresses, and the behavior of statically indeterminate members.

Shear & Moment Diagrams

Build shear and moment diagrams from the load-shear-moment relations, locate maximum moment and inflection points, and read the AISC Table 3-23 standard cases.

Load-shear relation: $\dfrac{dV}{dx} = w(x)$; Slope of the shear diagram equals the distributed-load term $w$ (force/length), per handbook §1.6.7. A downward applied load enters as a negative $w$, so the shear drops across it. $w$ in $\text{k/ft}$, $V$ in $\text{kip}$.
Shear-moment relation: $\dfrac{dM}{dx} = V(x)$; Slope of the moment diagram equals the shear. Maximum moment occurs where $V=0$. $M$ in $\text{kip-ft}$.
Shear from load area: $V_2 - V_1 = \int_{x_1}^{x_2}\! w\,dx$; Change in shear between two sections equals the area of the load diagram (handbook §1.6.7). With a downward load taken as negative $w$, the integral is negative, so the shear drops by the magnitude of that area.
Moment from shear area: $M_2 - M_1 = \int_{x_1}^{x_2}\! V\,dx$; Change in moment equals the area under the shear diagram between two sections.
Simply supported, full UDL: $V_{max}=\dfrac{wL}{2},\quad M_{max}=\dfrac{wL^2}{8}$; $M_{max}$ at midspan. $w$ in $\text{k/ft}$, $L$ in $\text{ft}$. AISC Table 3-23.
Simply supported, central point load: $V_{max}=\dfrac{P}{2},\quad M_{max}=\dfrac{PL}{4}$; $M_{max}$ at midspan under the load. $P$ in $\text{kip}$.
Simply supported, off-center point load: $M_{max}=\dfrac{P\,a\,b}{L}$; Load $P$ at distance $a$ from left, $b$ from right, $a+b=L$. Max moment under the load.
Cantilever, tip point load: $V_{max}=P,\quad M_{max}=PL$; Maximum (hogging) moment at the fixed end. $L$ = cantilever length.
Cantilever, full UDL: $V_{max}=wL,\quad M_{max}=\dfrac{wL^2}{2}$; Hogging at the fixed end. Note the factor is $1/2$, not $1/8$.
Overhang back-moment: $M_{support}= -\dfrac{w\,L_o^{2}}{2}$; Hogging moment delivered to the support by an overhang of length $L_o$ carrying UDL $w$.

Where it lives: NCEES PE Civil Reference Handbook — §4.1.7 Moment, Shear, and Deflection Diagrams · NCEES PE Civil Reference Handbook — §1.6.7 Beams (load-shear-moment relations and sign conventions) · AISC Steel Construction Manual, 15th ed. — Table 3-23, Shears, Moments and Deflections

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Deflection
5% of the exam

Beam and frame deflections by double integration, moment-area, conjugate-beam, and virtual-work methods; standard deflection formulas for common loadings; and serviceability deflection limits.

Deflection by Virtual Work (Unit Load)

The unit-load (virtual-work) method for the deflection of any truss joint ($\Sigma nNL/AE$) or beam/frame point ($\int mM/EI\,dx$), and how to choose the virtual system.

External virtual work = internal virtual work: $1\cdot\Delta = \sum n\,\delta_{\text{real}}$; The defining statement: a unit load does external work $1\cdot\Delta$ equal to the internal work of virtual forces through real deformations.
Truss joint deflection: $\Delta = \sum \dfrac{n\,N\,L}{A\,E}$; $n$ = member force from unit load, $N$ = member force from real loads (tension +), $L$ = length, $A$ = area, $E$ = modulus. Result is the displacement at and along the unit load.
Beam/frame deflection: $\Delta = \sum \int_0^{L} \dfrac{m(x)\,M(x)}{E I}\,dx$; $m(x)$ = moment from a unit load (force for deflection, couple for rotation); $M(x)$ = moment from real loads; integrate over each member.
Real member elongation (load): $(\Delta L) = \dfrac{N\,L}{A\,E}$; Axial deformation of a truss member under the real load; the real-deformation term inside the truss sum.
Real member elongation (temperature): $(\Delta L) = \alpha\,\Delta T\,L$; $\alpha$ = coefficient of thermal expansion, $\Delta T$ = temperature change. Substitutes for $NL/AE$ to get thermal deflection by the same unit-load sum.
Rotation by a unit couple: $\theta = \sum \int_0^{L} \dfrac{m_\theta(x)\,M(x)}{E I}\,dx$; Apply a unit moment at the point of desired rotation; $m_\theta(x)$ is the resulting virtual-moment diagram.
Combined axial + flexural work: $\Delta = \sum \dfrac{n\,N\,L}{A\,E} + \sum \int_0^{L}\dfrac{m\,M}{E I}\,dx$; Frames with significant axial force keep both terms; usually the bending term dominates and the axial term is dropped.
Diagram multiplication (Vereshchagin): $\int_0^L \dfrac{m\,M}{EI}\,dx = \dfrac{A_M\,\bar{m}}{EI}$; When $m(x)$ is linear, the integral equals the area $A_M$ of the real $M$ diagram times the ordinate $\bar{m}$ of the virtual diagram at the centroid of $A_M$, over $EI$.

Where it lives: NCEES PE Civil Reference Handbook — §4.1.4 Truss Deflection by Unit Load Method · NCEES PE Civil Reference Handbook — §4.1.5 Frame Deflection by Unit Load Method · Hibbeler, Structural Analysis

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Buckling, Torsion & Special Effects
6% of the exam

Euler and inelastic column buckling, effective length, torsion of shafts and members, fatigue, thermal deformation, bearing, and progressive-collapse considerations.

Euler Column Buckling & Effective Length

The Euler critical load, the effective-length factor K for ideal end conditions, the radius of gyration and slenderness KL/r, and the critical stress.

Euler critical load: $P_{cr} = \dfrac{\pi^2 E I}{(KL)^2}$; Elastic buckling load (kips). $E$ = modulus (ksi), $I$ = moment of inertia about the buckling axis (in$^4$), $K$ = effective-length factor, $L$ = unbraced length (in).
Effective length: $L_e = KL$; Distance between inflection points of the buckled shape; the equivalent pinned-pinned length.
Theoretical K factors: $K = 1.0,\ 0.5,\ 0.7,\ 2.0$; Pinned-pinned, fixed-fixed, fixed-pinned, fixed-free respectively (NCEES handbook §1.6.8 Columns). AISC recommended design values are larger: 0.65, 0.80, 1.0, 2.10 for fixed-fixed, fixed-pinned, pinned-pinned, fixed-free.
Radius of gyration: $r = \sqrt{\dfrac{I}{A}}$; Spread of area about the buckling axis (in). Use the smaller (weak-axis) value unless that axis is braced.
Effective slenderness ratio: $\lambda = \dfrac{KL}{r}$; Dimensionless governing parameter; the column buckles about the axis with the larger $KL/r$.
Critical (Euler) stress: $\sigma_{cr} = \dfrac{\pi^2 E}{(KL/r)^2}$; Buckling stress (ksi); depends only on $E$ and $KL/r$, NOT on $F_y$. Valid only while $\sigma_{cr} < F_y$.
Squash (yield) load: $P_y = F_y A$; Upper bound on capacity (kips); buckling governs when $P_{cr} < P_y$.
Inelastic-elastic transition (AISC 360-16): $\dfrac{KL}{r}\Big|_{\text{trans}} = 4.71\sqrt{\dfrac{E}{F_y}}$; Above this slenderness elastic buckling governs ($F_{cr}=0.877F_e$); below it inelastic buckling/yielding governs. About 113 for $F_y=50$ ksi.

Where it lives: NCEES PE Civil Reference Handbook — §1.6.8 Columns (Chapter 1 General Engineering; Euler's Formula and theoretical K) · AISC 360-16, Chapter E — Design of Members for Compression (Steel Construction Manual, 15th ed.) · Hibbeler, Mechanics of Materials, 10th ed. — column buckling background

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Structural Materials & Testing
8% of the exam

Engineering properties of concrete, steel, timber, and masonry; stress-strain behavior and modulus; concrete strength and mix; and material test methods (compression, tension, slump) and specification conformance.

Concrete Properties, Modulus & Strength

Specified compressive strength f′c, the elastic modulus Ec = 57000√f′c (psi), modulus of rupture, the stress-strain curve, β1, mix proportioning, and reinforcement grades.

Elastic modulus (normalweight): $E_c = 57{,}000\sqrt{f'_c}\ \text{(psi)}$; Secant modulus of normalweight concrete. $f'_c$ and $E_c$ both in psi; e.g., $f'_c=4{,}000\,\text{psi}\Rightarrow E_c\approx 3{,}605\,\text{ksi}$.
Elastic modulus (general, by unit weight): $E_c = 33\,w_c^{1.5}\sqrt{f'_c}\ \text{(psi)}$; $w_c$ = unit weight (pcf), $90\le w_c\le 160$. Reduces to the $57{,}000$ form at $w_c=145\,\text{pcf}$; use for lightweight concrete.
Modulus of rupture: $f_r = 7.5\,\lambda\sqrt{f'_c}\ \text{(psi)}$; Flexural tensile strength. $\lambda=1.0$ normalweight; smaller for lightweight. Drives the cracking moment and minimum-steel check.
Cracking moment: $M_{cr} = \dfrac{f_r\,I_g}{y_t}$; $I_g$ = gross moment of inertia, $y_t$ = distance from centroid to tension face. Used in effective-moment-of-inertia deflection.
Stress-block factor β1: $\beta_1 = 0.85 - 0.05\dfrac{f'_c - 4000}{1000}\quad (4000<f'_c<8000\ \text{psi})$; Depth of equivalent block $a=\beta_1 c$. $\beta_1=0.85$ for $f'_c\le4{,}000$, floor $0.65$ at $f'_c\ge8{,}000$ psi.
Equivalent compression stress: $C = 0.85\,f'_c\,b\,a$; Resultant compression on the Whitney block; the $0.85$ stress intensity is constant (does not change with $f'_c$).
Design crushing strain: $\varepsilon_{cu} = 0.003$; ACI extreme-fiber compression strain at flexural failure; anchors strain compatibility.
Reinforcement modulus: $E_s = 29{,}000\ \text{ksi}$; Same as structural steel; gives modular ratio $n=E_s/E_c \approx 7$ to $9$.
Modular ratio: $n = \dfrac{E_s}{E_c}$; Used to transform steel area to equivalent concrete in cracked-section (service) analysis.
Bar size to diameter: $d_b = \dfrac{\#}{8}\ \text{in (imperial bars)}$; For #3 through #8, a #n bar is n eighth-inches in diameter (#8 = 1.00 in, $A_b=0.79\,\text{in}^2$; #4 = 0.50 in); #9-#11 are larger and no longer follow the eighths rule. From handbook §4.3.1.

Where it lives: NCEES PE Civil Reference Handbook — §4.3 Concrete (Ec, β1 definitions, §4.3.1 bar areas) · ACI 318-14, Building Code Requirements for Structural Concrete — §19.2 (Ec, fr) and §22.2 (equivalent stress block, β1) · ACI 211.1, Standard Practice for Selecting Proportions for Normal, Heavyweight, and Mass Concrete

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Soil Properties & Classification
5% of the exam

Phase relationships and index properties, USCS and AASHTO classification, shear strength, permeability, compressibility and consolidation, lateral earth-pressure coefficients, and bearing-capacity parameters.

Soil Phase Relationships & Classification

The weight-volume phase diagram (e, w, S, unit weights) tied to USCS and AASHTO classification with the group index — the foundation every geotech calc rests on.

Void ratio and porosity: $e = \dfrac{V_v}{V_s}, \qquad n = \dfrac{e}{1+e}, \qquad e = \dfrac{n}{1-n}$; $e$ = void ratio (used in consolidation), $n$ = porosity. Both dimensionless; voids = water + air.
Bridge identity: $S\,e = w\,G_s$; Ties saturation $S$ and void ratio $e$ to water content $w$ and specific gravity $G_s$. Use $S$ and $w$ as decimals.
Dry unit weight: $\gamma_d = \dfrac{G_s\,\gamma_w}{1+e}$; Weight of solids per total volume. $\gamma_w = 62.4\,\text{pcf}$ ($9.81\,\text{kN/m}^3$).
Total (moist) unit weight: $\gamma_t = \gamma_d(1+w) = \dfrac{(G_s + S e)\gamma_w}{1+e}$; What a field sample weighs at water content $w$ and saturation $S$.
Saturated and buoyant unit weight: $\gamma_{sat} = \dfrac{(G_s+e)\gamma_w}{1+e}, \qquad \gamma_b = \gamma_{sat} - \gamma_w$; $\gamma_{sat}$ at $S=1$; $\gamma_b$ (submerged/effective) governs effective stress below the water table.
Grading coefficients: $C_u = \dfrac{D_{60}}{D_{10}}, \qquad C_c = \dfrac{D_{30}^{\,2}}{D_{10}\,D_{60}}$; $D_{xx}$ = grain size with $xx\%$ passing. Well-graded sand needs $C_u\ge6$, gravel $C_u\ge4$, both with $1\le C_c\le3$.
Plasticity index and A-line: $PI = LL - PL, \qquad PI_{A} = 0.73\,(LL-20)$; On/above A-line with $PI>7\Rightarrow$ clay (C); below $\Rightarrow$ silt (M). $LL<50$ low (L), $\ge50$ high (H).
Liquidity index: $LI = \dfrac{w - PL}{PI}$; Locates in-situ water content between the plastic ($LI=0$) and liquid ($LI=1$) limits; $LI>1$ flags sensitive clay.
AASHTO group index: $GI = (F-35)\big[0.2+0.005(LL-40)\big] + 0.01(F-15)(PI-10)$; $F$ = % passing No. 200. Round to nearest integer; report 0 if negative. A-2-6/A-2-7 use only the last term.
Relative density: $D_r = \dfrac{e_{max}-e}{e_{max}-e_{min}} \times 100\%$; Density state of a coarse soil between its loosest ($e_{max}$) and densest ($e_{min}$) states.

Where it lives: NCEES PE Civil Reference Handbook — §3.7 Soil Classification and Boring Log Interpretation · ASTM D2487 — Unified Soil Classification System (USCS) · AASHTO M145 — Classification of Soils and Soil-Aggregate Mixtures (group index) · FHWA-NHI-06-088 Soils and Foundations, Vol. I

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Reinforced & Prestressed Concrete
9% of the exam

ACI flexural and shear strength of beams and one-way slabs, reinforcement ratio limits and development length, short-column axial capacity, and prestressed-concrete service stresses and prestress losses.

ACI Flexural Design of RC Beams

The Whitney stress block, nominal moment $M_n$ of a singly-reinforced beam, the tension-controlled $\phi=0.90$, and the $\rho_{min}$/$\rho_{max}$ limits that keep failures ductile.

Stress-block depth: $a = \dfrac{A_s f_y}{0.85\, f'_c\, b}$; Depth of the equivalent rectangular compression block. $A_s$ (in²), $f_y$, $f'_c$ (psi), $b$ (in); $a$ in inches. From force balance $C=T$.
Block factor β₁: $\beta_1 = \begin{cases} 0.85 & f'_c \le 4000 \\ 0.85 - 0.05\dfrac{f'_c-4000}{1000} & 4000 < f'_c \le 8000 \\ 0.65 & f'_c > 8000 \end{cases}$; Ratio of block depth $a$ to neutral-axis depth $c$ (ACI 318-14 Table 22.2.2.4.3). $f'_c$ in psi.
Nominal moment: $M_n = A_s f_y\!\left(d - \dfrac{a}{2}\right)$; Internal couple of the section. Lever arm $d-a/2$ in inches → $M_n$ in $\text{lb}\cdot\text{in}$; divide by 12,000 for $\text{kip}\cdot\text{ft}$.
Design strength requirement: $\phi M_n \ge M_u, \qquad \phi = 0.90\ \text{(tension-controlled)}$; Strength condition. $\phi=0.90$ when $\varepsilon_t \ge 0.005$; transition between 0.65/0.75 and 0.90 otherwise.
Net tensile strain: $\varepsilon_t = 0.003\,\dfrac{d_t - c}{c}$; Strain in extreme tension steel from the linear strain diagram with $\varepsilon_{cu}=0.003$. $\ge 0.005$ → tension-controlled.
Minimum steel: $A_{s,min} = \max\!\left(\dfrac{3\sqrt{f'_c}}{f_y},\ \dfrac{200}{f_y}\right) b_w d$; ACI 318-14 §9.6.1; prevents brittle failure at cracking. $f'_c$, $f_y$ in psi; $\sqrt{f'_c}$ needs psi.
Reinforcement ratio: $\rho = \dfrac{A_s}{b\,d}$; Tension steel ratio; compare against $\rho_{min}=A_{s,min}/(b_w d)$ and the strain-limited $\rho_{max}$.
Maximum steel ratio (strain limit): $\rho_{max} = 0.85\,\beta_1\dfrac{f'_c}{f_y}\cdot\dfrac{0.003}{0.003+\varepsilon_{t,limit}}$; From $c$ at the strain limit ($\varepsilon_{t,limit}=0.004$ minimum, 0.005 to keep $\phi=0.90$). Caps the steel indirectly.
Resistance-factor (design) coefficient form: $M_u = \phi A_s f_y\!\left(d-\dfrac{a}{2}\right)$; Design equation solved for $A_s$ given $M_u$; quadratic in $A_s$ since $a$ depends on $A_s$.
Concrete modulus: $E_c = 57{,}000\sqrt{f'_c}\ \ (\text{psi})$; Normalweight-concrete modulus (ACI 318-14 §19.2.2). $f'_c$ in psi; needed for service/deflection checks.

Where it lives: NCEES PE Civil Reference Handbook — §4.3.2.2 Beams—Flexure Strength (equivalent rectangular stress block, β₁) · ACI 318-14, Building Code Requirements for Structural Concrete — §22.2 (flexural strength), §21.2 (φ factors), §9.6.1 (minimum reinforcement) · ACI 318-14 Table 22.2.2.4.3 — β₁ as a function of f′c

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Structural Steel Design
9% of the exam

AISC tension, compression, flexure, and shear member strength by LRFD and ASD, block shear, lateral-torsional buckling, beam-column interaction, and composite-beam behavior.

AISC Compression Member Strength

Compute the flexural-buckling strength of a steel column from KL/r: the elastic Fe, the inelastic/elastic Fcr branches at the 4.71 transition, and the LRFD/ASD strengths.

Governing slenderness: $\dfrac{KL}{r} = \max\left[\dfrac{K_xL_x}{r_x},\ \dfrac{K_yL_y}{r_y}\right]$; Larger of the two principal-axis values governs. $K$ = effective-length factor, $L$ = unbraced length, $r=\sqrt{I/A}$ (in). Keep $KL/r$ preferably below 200.
Elastic (Euler) buckling stress: $F_e = \dfrac{\pi^2 E}{\left(KL/r\right)^2}$; $E = 29{,}000$ ksi for steel. $F_e$ in ksi. Independent of $F_y$. AISC 360-16 Eq. E3-4.
Branch transition (inelastic/elastic): $\dfrac{KL}{r}\le 4.71\sqrt{\dfrac{E}{F_y}} \iff \dfrac{F_y}{F_e}\le 2.25$; Limit = 113 for $F_y=50$ ksi, 134 for $F_y=36$ ksi. At or below: inelastic branch; above: elastic branch.
Inelastic critical stress: $F_{cr} = \left(0.658^{\,F_y/F_e}\right)F_y$; AISC 360-16 Eq. E3-2, for $KL/r \le 4.71\sqrt{E/F_y}$. Approaches $F_y$ as the column gets stocky.
Elastic critical stress: $F_{cr} = 0.877\,F_e$; AISC 360-16 Eq. E3-3, for slender columns above the transition. The 0.877 covers initial out-of-straightness.
Nominal compressive strength: $P_n = F_{cr}\,A_g$; $A_g$ = gross area (in²); $P_n$ in kips. Use gross area — bolt holes do not reduce compression. AISC 360-16 Eq. E3-1.
LRFD design strength: $\phi_c P_n,\qquad \phi_c = 0.90$; Compare to factored load $P_u$ from ASCE 7-16 LRFD combinations. Require $\phi_c P_n \ge P_u$.
ASD allowable strength: $\dfrac{P_n}{\Omega_c},\qquad \Omega_c = 1.67$; Compare to service load $P_a$ from ASD combinations. Require $P_n/\Omega_c \ge P_a$. Never mix with LRFD.
Equivalent weak-axis length for Table 4-1: $(KL)_{\text{eff},y} = \dfrac{K_x L_x}{r_x/r_y}$; Converts a strong-axis effective length to the $y$-axis basis the table uses, so you enter Table 4-1 with the larger of $K_yL_y$ and this value.

Where it lives: AISC 360-16 — Specification for Structural Steel Buildings, Chapter E (Design of Members for Compression) · AISC Steel Construction Manual, 15th ed. — Table 4-1 (Available Strength in Axial Compression) · NCEES PE Civil Reference Handbook v2.2 — §4.2 Steel

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Timber (Wood) Design
4% of the exam

NDS allowable-stress design of sawn-lumber and glulam beams and columns, adjustment factors, bending and horizontal shear, bearing, stability, and combined bending and axial loads.

NDS Timber Design: Adjustment Factors

How the NDS reference design values become adjusted (allowable) values F' through the chain of adjustment factors — CD, CM, Ct, CF, CL, CP, Cr and the rest.

Adjusted bending value: $F'_b = F_b\,C_D\,C_M\,C_t\,C_L\,C_F\,C_{fu}\,C_i\,C_r$; Reference $F_b$ (psi) times every applicable factor; $C_L$ is the beam-stability factor, $C_F$ the size factor (sawn) or $C_V$ the volume factor (glulam — use only the smaller of $C_L$, $C_V$).
Adjusted compression (parallel): $F'_c = F_c\,C_D\,C_M\,C_t\,C_F\,C_i\,C_P = F^{*}_c\,C_P$; $F^{*}_c$ is every factor except $C_P$; the column-stability factor $C_P$ is computed last from $F_{cE}/F^{*}_c$.
Adjusted shear value: $F'_v = F_v\,C_D\,C_M\,C_t\,C_i$; Horizontal shear; takes duration and service factors but NOT $C_F$, $C_L$, or $C_r$.
Adjusted bearing (perp. to grain): $F'_{c\perp} = F_{c\perp}\,C_M\,C_t\,C_i\,C_b$; Bearing perpendicular to grain; $C_b$ is the bearing-area factor. Note: NO load-duration factor $C_D$ and NO size factor.
Adjusted modulus (stability): $E'_{min} = E_{min}\,C_M\,C_t\,C_i$; Feeds $F_{cE}$ and $F_{bE}$. Elasticity is duration-independent, so no $C_D$ and no $C_F$ ever apply to $E$ or $E_{min}$.
Starred reference (pre-stability): $F^{*}_b = F_b\,C_D\,C_M\,C_t\,C_F\,C_{fu}\,C_i\,C_r$; All factors except $C_L$; the ratio $F_{bE}/F^{*}_b$ then yields $C_L$. Same idea for $F^{*}_c$ and $C_P$.
Load-duration factor values: $C_D = 0.9,\ 1.0,\ 1.15,\ 1.25,\ 1.6,\ 2.0$; Permanent, 10-yr (normal), snow, 7-day/construction, wind/seismic, impact. Use the shortest-duration load in each combination.
Repetitive-member factor: $C_r = 1.15$; Applies to $F_b$ only when 3+ parallel members spaced $\le 24$ in. share load through a deck (joists, studs, rafters).
ASD demand-to-capacity: $f \le F' \quad\Longleftrightarrow\quad \dfrac{f}{F'} \le 1.0$; The ASD check: actual stress $f$ (e.g., $f_b = M/S$) must not exceed the adjusted allowable $F'$. Never mix in LRFD $\phi$-factors.

Where it lives: AWC National Design Specification (NDS) for Wood Construction, 2018 edition (ASD method) — Ch. 2 general adjustment factors + Ch. 4/5 applicability tables · NDS Supplement, 2018 — Design Values for Wood Construction (reference $F_b$, $F_v$, $F_c$, $F_{c\perp}$, $E$, $E_{min}$ and size factors $C_F$) · AWC NDS 2018 Table 4.3.1 (sawn lumber) and Table 5.3.1 (glulam) — adjustment-factor applicability grids

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Masonry Design
4% of the exam

TMS allowable-stress design of reinforced and unreinforced CMU and brick: flexure, shear, axial and slender-wall capacity, reinforcement, and brick-veneer anchorage.

TMS 402 Masonry: ASD Flexure & Axial

Allowable-stress flexure and axial design of concrete masonry per TMS 402-16: Fb, the slenderness-reduced axial capacity, the cracked-transformed flexure check, and the combined unity equation.

Allowable flexural compressive stress (reinforced): $F_b = 0.45\,f'_m$; Reinforced masonry ASD bending limit (TMS 402-16 §8.3.4.2.2, Eq. 8-21). $f'_m$ in psi. The $\tfrac{1}{3}f'_m$ coefficient is the unreinforced-flexure allowable and the $F_a$ axial coefficient, not this value.
Allowable steel tensile stress: $F_s = 32\,\text{ksi}$; Grade 60 reinforcement, ASD (Grade 40/50 → 20 ksi). Used in $M_s = A_s F_s j d$.
Modular ratio: $n = \dfrac{E_s}{E_m} = \dfrac{29{,}000\,\text{ksi}}{900\,f'_m}$; $E_m = 900 f'_m$ for CMU. At $f'_m = 2000\,\text{psi}$, $n \approx 16.1$ (much larger than concrete's ~8).
Radius of gyration, solid wall: $r = \dfrac{t}{\sqrt{12}}$; Net thickness $t$ (in). 8-in CMU: $t = 7.625\,\text{in}$, $r \approx 2.20\,\text{in}$.
Allowable axial force (slender): $P_a = \left(0.25 f'_m A_n + 0.65 A_{st} F_s\right)\!\left[1-\left(\tfrac{h}{140 r}\right)^2\right]$; For $h/r \le 99$. $A_n$ = net area, $A_{st}$ = longitudinal steel. (For $h/r > 99$, use $(70r/h)^2$.)
Axial capacity, very slender: $P_a = \left(0.25 f'_m A_n + 0.65 A_{st} F_s\right)\!\left(\tfrac{70 r}{h}\right)^2$; Use when $h/r > 99$ (Euler-controlled branch).
Allowable axial stress: $F_a = \tfrac{1}{3}f'_m\!\left[1-\left(\tfrac{h}{140 r}\right)^2\right]$; Reinforced allowable axial stress (TMS 402-16 §8.3.4.2.1, $h/r \le 99$). This is the $\tfrac{1}{3}f'_m$ coefficient — used in the unity equation as the $f_a/F_a$ denominator, not as the bending allowable.
Unreinforced flexure check: $f_b = \dfrac{M}{S} \le F_t$; $F_t$ = allowable flexural tension from TMS 402-16 Table 8.2.4.2 (mortar/grout/direction); $S$ = net section modulus. Unreinforced flexural-compression allowable is $\tfrac{1}{3}f'_m$ (§8.2.4.2).
Cracked neutral-axis ratio: $k = \sqrt{2\rho n + (\rho n)^2} - \rho n, \quad \rho = \dfrac{A_s}{bd}$; Working-stress cracked transformed section for reinforced flexure.
Lever-arm ratio: $j = 1 - \dfrac{k}{3}$; Internal moment arm $= jd$. Often $j \approx 0.9$ for typical wall reinforcement.
Allowable reinforced moment: $M_{\text{allow}} = \min\!\left(A_s F_s\,j\,d,\ \tfrac{1}{2}F_b\,k\,j\,b\,d^2\right), \quad F_b = 0.45 f'_m$; Smaller of steel-controlled and masonry-controlled allowable moment; masonry side uses $F_b = 0.45 f'_m$.
Unity (interaction) equation: $\dfrac{f_a}{F_a} + \dfrac{f_b}{F_b} \le 1.0$; $f_a = P/A_n$, $F_a = \tfrac{1}{3}f'_m[1-(h/140r)^2]$, $f_b$ = flexural compressive stress, $F_b = 0.45 f'_m$.
Eccentric Euler buckling check: $P \le \tfrac{1}{4}P_e, \quad P_e = \dfrac{\pi^2 E_m I_n}{h^2}\!\left(1 - 0.577\tfrac{e}{r}\right)^{3}$; Independent stability check on eccentric axial load; $e$ = load eccentricity, $I_n$ = net moment of inertia.

Where it lives: TMS 402-16 — Building Code Requirements for Masonry Structures, §8.2 (Unreinforced) and §8.3 (Reinforced), Allowable Stress Design · TMS 402-16 §8.3.4.2.2 — Reinforced flexural compressive stress $F_b = 0.45 f'_m$ (Eq. 8-21) and combined unity interaction · TMS 402-16 §8.3.4.2.1 — Allowable axial stress $F_a = \tfrac{1}{3}f'_m[1-(h/140r)^2]$ and allowable axial force $P_a$ · TMS 402-16 §8.2.4.2 — Allowable flexural tensile and unreinforced flexural compressive ($\tfrac{1}{3}f'_m$) stresses · ASCE 7-16 — Minimum Design Loads (service-load combinations applied to ASD masonry checks)

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Connections
6% of the exam

Bolted and welded steel connections, bearing and slip-critical bolts, weld strength, block shear, and embedded, anchored, and post-installed anchors in concrete.

AISC Bolted Connections (Shear, Bearing, Slip)

Bolt shear strength, bearing and tearout at the holes, bearing vs slip-critical behavior, and how the bolt-group capacity is the sum of per-bolt limit states.

Bolt shear strength: $\phi R_n = \phi\,F_{nv}\,A_b\,m$; Per bolt. $F_{nv}=54$ ksi (A325-N) / $68$ (A325-X or A490-N) / $84$ (A490-X); $A_b=\pi d^2/4$ (in²); $m$ = shear planes; $\phi=0.75$.
Bolt nominal area: $A_b = \dfrac{\pi d^2}{4}$; Gross shank area from nominal diameter $d$ (in); a 3/4-in bolt has $A_b=0.442\,\text{in}^2$, a 7/8-in bolt $0.601\,\text{in}^2$.
Bearing strength at a hole: $\phi R_n = \phi\,2.4\,d\,t\,F_u$; Deformation-considered upper limit. $d$ = bolt dia, $t$ = ply thickness, $F_u$ = ply tensile strength (ksi); $\phi=0.75$.
Tearout strength at a hole: $\phi R_n = \phi\,1.2\,l_c\,t\,F_u$; $l_c$ = clear distance to next hole or edge in line of force = $l_e$ or $s$ minus the std hole diameter $d_h$ ($d+\tfrac{1}{16}$ in for $d\le\tfrac78$ in, $d+\tfrac18$ in for $d\ge1$ in, AISC Table J3.3).
Controlling bearing/tearout per bolt: $\phi R_n = \phi\min(2.4\,d\,t\,F_u,\ 1.2\,l_c\,t\,F_u)$; Take the smaller; tearout usually governs at edge bolts (small $l_c$), bearing at interior bolts.
Slip-critical design resistance: $\phi R_n = \phi\,\mu\,D_u\,h_f\,T_b\,n_s$; $\mu=0.30$ (A), $0.50$ (B); $D_u=1.13$; $h_f=1.0$ (no filler); $T_b$ from Table J3.1; $n_s$ = slip planes; $\phi=1.00$ std holes.
Minimum pretension (Table J3.1, sample): $T_b\!: \ \tfrac{3}{4}''\,\text{A325}=28,\ \tfrac{7}{8}''\,\text{A325}=39,\ \tfrac{7}{8}''\,\text{A490}=49\ \text{kips}$; Specified minimum pretension for fully tensioned high-strength bolts (kips); required for SC and for fatigue/seismic joints.
Block shear rupture: $\phi R_n = \phi\big(0.6 F_u A_{nv} + U_{bs}F_u A_{nt}\big) \le \phi\big(0.6 F_y A_{gv} + U_{bs}F_u A_{nt}\big)$; $A_{nv},A_{gv}$ net/gross shear area; $A_{nt}$ net tension area; $U_{bs}=1.0$ uniform tension; $\phi=0.75$.
Group capacity (concentric): $\phi R_{n,\text{group}} = N_b \times \min(\phi R_n)_{\text{per bolt}}$; Equal sharing only when the load passes through the group centroid; eccentric groups use the elastic-vector or IC method.
Standard hole diameter: $d_h = d + \tfrac{1}{16}\ \text{in}\ (d\le\tfrac78''),\quad d+\tfrac18\ \text{in}\ (d\ge1'')$; Standard round hole per AISC Table J3.3; oversized and slotted holes are larger and reduce SC $\phi$ and bearing/tearout $l_c$.

Where it lives: AISC 360-16 Specification for Structural Steel Buildings — Chapter J (J3 bolts, J3.6–J3.8 shear/slip, J3.10 bearing, J4.3 block shear) · AISC Steel Construction Manual, 15th ed. — Part 7 (bolting) and Tables 7-1 to 7-6 (available bolt strengths) · NCEES PE Civil Reference Handbook — §4.2.1 Fastener Groups in Shear (group geometry only; no strength values)

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Foundations & Retaining Walls
8% of the exam

Bearing capacity and settlement of spread footings, combined footings and mats, pile and drilled-shaft capacity, and retaining-wall stability against sliding, overturning, and bearing.

Shallow Foundation Bearing Capacity & Settlement

The general bearing-capacity equation with bearing-capacity, shape, depth and groundwater factors; net vs. gross allowable pressure with a factor of safety; and elastic plus consolidation settlement.

General bearing capacity (strip): $q_{ult} = c\,N_c + q\,N_q + \tfrac{1}{2}\gamma B_f N_\gamma$; Ultimate bearing pressure of a concentrically loaded strip footing. $q = \gamma_a D_f$ surcharge; $N_c, N_q, N_\gamma$ from the handbook table at $\phi$.
Bearing capacity with shape factors: $q_{ult} = c\,N_c s_c + q\,N_q s_q + \tfrac{1}{2}\gamma B_f N_\gamma s_\gamma$; Square/rectangular footing form; multiply each term by its AASHTO shape factor.
Shape factors (AASHTO): $s_c = 1 + \tfrac{B_f}{L_f}\tfrac{N_q}{N_c},\; s_q = 1 + \tfrac{B_f}{L_f}\tan\phi,\; s_\gamma = 1 - 0.4\tfrac{B_f}{L_f}$; $B_f/L_f = 1$ for a square footing, $\to 0$ for a strip. Per handbook §3.4.2.1.
Net allowable bearing: $q_{all,net} = \dfrac{q_{ult} - \gamma_a D_f}{FS}$; Apply $FS$ (typically 3) to the NET ultimate. Compare against net applied service pressure — same basis on both sides.
Clay (undrained) bearing: $q_{ult} = 5.14\,c_u\,s_c + \gamma_a D_f$; $\phi = 0$ case: $N_c = 5.14$, $N_q = 1$, $N_\gamma = 0$. $c_u$ = undrained shear strength.
Allowable column load: $Q_{all} = q_{all,net}\,A = q_{all,net}\,B_f L_f$; Net allowable pressure times footing plan area; the service load the footing can carry.
Elastic settlement: $\delta_v = C_d\,\Delta p\,B_f\,\dfrac{1 - \nu^2}{E_m}$; Immediate settlement (sand, stiff clay). $C_d$ from the shape/rigidity table; $E_m$ = soil modulus, $\nu$ = Poisson's ratio.
Consolidation settlement (NC): $S_c = \dfrac{C_c}{1 + e_0}H_0\log_{10}\dfrac{p_f}{p_o}$; Normally consolidated clay. $C_c$ compression index, $e_0$ initial void ratio, $H_0$ layer thickness, $p_f = p_o + \Delta p$.
Consolidation settlement (OC, below pc): $S_c = \dfrac{C_r}{1 + e_0}H_0\log_{10}\dfrac{p_f}{p_o}$; Overconsolidated clay with $p_f \le p_c$. Uses the recompression index $C_r \ll C_c$.
Consolidation settlement (OC, crossing pc): $S_c = \dfrac{C_r}{1+e_0}H_0\log\dfrac{p_c}{p_o} + \dfrac{C_c}{1+e_0}H_0\log\dfrac{p_f}{p_c}$; When $\Delta p$ pushes the stress past the preconsolidation pressure $p_c$; recompression then virgin.
Stress increase (2:1 method): $\Delta p = \dfrac{P}{(B_f + z)(L_f + z)}$; Approximate vertical stress at depth $z$ below the base; evaluate at clay mid-depth for settlement.

Where it lives: NCEES PE Civil Reference Handbook — §3.4 Bearing Capacity (general equation, factor and shape-factor tables) · NCEES PE Civil Reference Handbook — §3.5.2 Foundation Settlement (elastic method) · NCEES PE Civil Reference Handbook — §3.2 Consolidation (compression/recompression indices, NC/OC settlement) · FHWA-NHI-06-089, Soils and Foundations, Vol. II

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Temporary Structures & Safety
6% of the exam

Formwork and falsework lateral pressures, shoring and reshoring, scaffolding and bracing, anchorage, special inspections and submittals, construction impact on adjacent facilities, and OSHA construction safety.

Formwork Pressure, Shoring & Reshoring

The ACI 347 lateral pressure of fresh concrete on wall and column forms, how shores and reshores distribute construction loads through a multistory frame, and falsework basics.

Hydrostatic (full fluid) pressure: $p = w\,h$; Upper bound on form pressure if concrete never set; $w\approx150\ \text{pcf}$ normal weight, $h$ = depth of plastic concrete (ft). Result in psf.
ACI 347 wall pressure ($R\le 7$ ft/hr): $p_{max} = C_w C_c\!\left(150 + \dfrac{9000\,R}{T}\right)$; $R$ = placement rate (ft/hr), $T$ = concrete temperature ($^\circ$F), $C_w$ unit-weight coeff, $C_c$ chemistry coeff. psf.
Wall pressure bounds: $600\,C_w \le p_{max} \le C_w(150)h$; Floor of $600C_w$ psf and ceiling at the full fluid head $C_w(150)h$. Apply AFTER the formula.
ACI 347 column pressure: $p_{max} = C_w C_c\!\left(150 + \dfrac{9000\,R}{T}\right) \le 3000\,C_w$; Same rate term, but capped at $3000\,C_w$ psf (columns reach higher pressure than walls).
Depth to maximum pressure: $h_{p} = \dfrac{p_{max}}{150\,C_w}$; Depth (ft) at which the equivalent-fluid line reaches $p_{max}$; pressure is constant below this.
Resultant lateral load per unit width: $P = \tfrac{1}{2}p_{max}\,h_p + p_{max}\,(H - h_p)$; Area of the design pressure trapezoid (triangle to $h_p$, then constant to wall height $H$). lb per ft of wall.
Shoring design load: $w_{\text{shore}} = w_{\text{slab,fresh}} + w_{\text{forms}} + w_{LL,\text{constr}}$; Dead load of fresh slab + forms + construction live load (min $\sim50$ psf). Drives shore and falsework sizing.
Reshore load amplification: $Q_{\text{slab}} = \beta\,D_{\text{slab}}, \quad \beta \approx 1.5\text{–}2.0$; Grundy-Kabaila distribution: a supporting slab can carry $\beta$ times one slab dead load during placement above.
Falsework minimum lateral (stability) load: $H \ge 0.02\,\Sigma P$; Horizontal design load $\ge 2\%$ of total supported vertical load, for falsework stability/bracing.

Where it lives: ACI 347-14 (R2021) — Guide to Formwork for Concrete (lateral pressure $C_w$/$C_c$ formula, design loads) · ACI SP-4 / ACI 347R — Formwork for Concrete (resultant pressure diagrams, shoring/reshoring practice) · OSHA 29 CFR 1926 Subpart Q — Concrete and Masonry Construction (1926.700 formwork and shoring requirements) · Grundy & Kabaila, 'Construction Loads on Slabs with Shored Formwork in Multistory Buildings,' ACI Journal

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PE Civil: Structural formula sheet

Gravity Loads & Load Paths
9% of the exam

ASCE 7 Load Combinations (LRFD & ASD)

Wind, Seismic & Environmental Loads
8% of the exam

Seismic Base Shear (Equivalent Lateral Force)

Structural Analysis
13% of the exam

Shear & Moment Diagrams

Deflection
5% of the exam

Deflection by Virtual Work (Unit Load)

Buckling, Torsion & Special Effects
6% of the exam

Euler Column Buckling & Effective Length

Structural Materials & Testing
8% of the exam

Concrete Properties, Modulus & Strength

Soil Properties & Classification
5% of the exam

Soil Phase Relationships & Classification

Reinforced & Prestressed Concrete
9% of the exam

ACI Flexural Design of RC Beams

Structural Steel Design
9% of the exam

AISC Compression Member Strength

Timber (Wood) Design
4% of the exam

NDS Timber Design: Adjustment Factors

Masonry Design
4% of the exam

TMS 402 Masonry: ASD Flexure & Axial

Connections
6% of the exam

AISC Bolted Connections (Shear, Bearing, Slip)

Foundations & Retaining Walls
8% of the exam

Shallow Foundation Bearing Capacity & Settlement

Temporary Structures & Safety
6% of the exam

Formwork Pressure, Shoring & Reshoring

Now use them on real questions

Gravity Loads & Load Paths9% of the exam

ASCE 7 Load Combinations (LRFD & ASD)

Wind, Seismic & Environmental Loads8% of the exam

Seismic Base Shear (Equivalent Lateral Force)

Structural Analysis13% of the exam

Shear & Moment Diagrams

Deflection5% of the exam

Deflection by Virtual Work (Unit Load)

Buckling, Torsion & Special Effects6% of the exam

Euler Column Buckling & Effective Length

Structural Materials & Testing8% of the exam

Concrete Properties, Modulus & Strength

Soil Properties & Classification5% of the exam

Soil Phase Relationships & Classification

Reinforced & Prestressed Concrete9% of the exam

ACI Flexural Design of RC Beams

Structural Steel Design9% of the exam

AISC Compression Member Strength

Timber (Wood) Design4% of the exam

NDS Timber Design: Adjustment Factors

Masonry Design4% of the exam

TMS 402 Masonry: ASD Flexure & Axial

Connections6% of the exam

AISC Bolted Connections (Shear, Bearing, Slip)

Foundations & Retaining Walls8% of the exam

Shallow Foundation Bearing Capacity & Settlement

Temporary Structures & Safety6% of the exam

Formwork Pressure, Shoring & Reshoring

Now use them on real questions

Gravity Loads & Load Paths
9% of the exam

Wind, Seismic & Environmental Loads
8% of the exam

Structural Analysis
13% of the exam

Deflection
5% of the exam

Buckling, Torsion & Special Effects
6% of the exam

Structural Materials & Testing
8% of the exam

Soil Properties & Classification
5% of the exam

Reinforced & Prestressed Concrete
9% of the exam

Structural Steel Design
9% of the exam

Timber (Wood) Design
4% of the exam

Masonry Design
4% of the exam

Connections
6% of the exam

Foundations & Retaining Walls
8% of the exam

Temporary Structures & Safety
6% of the exam