Structural Engineering Exam (SE) Vertical Forces (Gravity/Other) — Buildings Depth Syllabus

What is the ACI 318 development length for a standard hooked bar in tension, $\ell_{dh}$ (basic form)?

$$\ell_{dh} = \frac{f_y\,\psi_e\psi_c\psi_r\psi_o}{55\,\lambda\sqrt{f'_c}}\,d_b^{1.5}$$ but not less than $8 d_b$ or $6$ in. (psi units).

For a steel tension member (AISC 360), give the two limit-state nominal strengths and their $\phi$ factors.

Yielding on the gross section: $P_n = F_y A_g$, $\phi_t = 0.90$. Rupture on the net effective section: $P_n = F_u A_e$, $\phi_t = 0.75$. Design strength is the lesser of the two.

How is the effective net area $A_e$ of a tension member computed, and what does the shear lag factor $U$ represent?

$A_e = U A_n$, where $A_n$ is the net area (gross minus hole areas) and $U$ is the shear lag factor accounting for non-uniform stress when not all elements of the cross-section are connected. A common form is $U = 1 - \bar{x}/L$.

In computing net width across a chain of staggered bolt holes (AISC), what term is added for each diagonal segment?

For each staggered gage segment add $\dfrac{s^2}{4g}$ to the net width, where $s$ is the longitudinal spacing (pitch) and $g$ the transverse gage. Net width $= w_g - \sum d_h + \sum \dfrac{s^2}{4g}$.

For a steel compression member (AISC 360), what slenderness parameter determines whether flexural buckling is inelastic or elastic, and what is the elastic (Euler) critical stress?

Compare $\dfrac{KL}{r}$ to $4.71\sqrt{E/F_y}$ (equivalently $F_y/F_e \leq 2.25$). The elastic buckling stress is $$F_e = \frac{\pi^2 E}{\left(\dfrac{KL}{r}\right)^2}.$$

State the AISC 360 flexural buckling stress equations for the inelastic and elastic ranges.

Inelastic ($\tfrac{KL}{r} \leq 4.71\sqrt{E/F_y}$): $F_{cr} = \left(0.658^{\,F_y/F_e}\right)F_y$. Elastic ($> 4.71\sqrt{E/F_y}$): $F_{cr} = 0.877 F_e$. Then $P_n = F_{cr} A_g$, $\phi_c = 0.90$.

What are the effective length factor $K$ recommended (theoretical) values for: fixed-fixed, fixed-pinned, pinned-pinned, and fixed-free columns?

Fixed-fixed $K=0.5$; fixed-pinned $K=0.7$; pinned-pinned $K=1.0$; fixed-free (cantilever) $K=2.0$. (Recommended design values are slightly higher than theoretical.)

For a compact, laterally supported steel I-beam (AISC 360), what is the nominal flexural strength $M_n$, and the design factor?

Yielding governs: $M_n = M_p = F_y Z_x$, where $Z_x$ is the plastic section modulus. $\phi_b = 0.90$. This applies when $L_b \leq L_p$ (full plastic moment, no LTB).

Define the lateral-torsional buckling limits $L_p$ and $L_r$ and the three flexural strength zones for an I-shaped beam.

$L_p$ = unbraced length limit for full plastic moment; $L_r$ = limit for inelastic LTB. Zone 1 ($L_b \leq L_p$): $M_n = M_p$. Zone 2 ($L_p < L_b \leq L_r$): inelastic LTB, linear interpolation. Zone 3 ($L_b > L_r$): elastic LTB, $M_n = F_{cr} S_x \leq M_p$.

What is the role of the lateral-torsional buckling modification factor $C_b$, and its value for a uniform moment?

$C_b$ accounts for moment gradient over the unbraced length, increasing LTB capacity for non-uniform moment. $C_b = 1.0$ for uniform moment. The general formula is $$C_b = \frac{12.5 M_{max}}{2.5 M_{max} + 3 M_A + 4 M_B + 3 M_C}.$$

State the AISC 360 beam-column interaction equations (combined axial + flexure).

For $\dfrac{P_r}{P_c} \geq 0.2$: $$\frac{P_r}{P_c} + \frac{8}{9}\left(\frac{M_{rx}}{M_{cx}} + \frac{M_{ry}}{M_{cy}}\right) \leq 1.0.$$ For $\dfrac{P_r}{P_c} < 0.2$: $$\frac{P_r}{2P_c} + \left(\frac{M_{rx}}{M_{cx}} + \frac{M_{ry}}{M_{cy}}\right) \leq 1.0.$$

In second-order analysis of beam-columns, what do the $B_1$ and $B_2$ amplification factors (AISC) represent?

$B_1$ amplifies for the $P\text{-}\delta$ effect (member curvature, no joint translation): $B_1 = \dfrac{C_m}{1 - \alpha P_r/P_{e1}} \geq 1$. $B_2$ amplifies for the $P\text{-}\Delta$ effect (lateral joint translation/sidesway).

For a composite steel-concrete beam with full shear connection, where is the plastic neutral axis (PNA) when the concrete slab can resist the full steel tension force?

The PNA lies within the slab when $0.85 f'_c\,A_c \geq F_y A_s$, i.e. the concrete compressive capacity exceeds the steel's tensile yield force. The effective concrete compression force is $C = F_y A_s$ (full steel yield governs).

How is the total horizontal shear force transferred by shear studs determined for a fully composite beam (positive moment)?

$V' = \min\left(0.85 f'_c A_c,\ F_y A_s\right)$. The number of studs between max moment and zero moment is $N = V'/Q_n$, where $Q_n$ is the nominal strength of one stud connector.

For a high-strength bolt in a bearing-type connection (AISC), give the nominal shear and tensile strengths.

Shear: $R_n = F_{nv} A_b$ (per shear plane). Tension: $R_n = F_{nt} A_b$. $A_b$ is the nominal bolt area; $F_{nv}$, $F_{nt}$ are nominal shear/tensile stresses (e.g., for A325-X, $F_{nv}=68$ ksi). $\phi = 0.75$.

What is the AISC bolt bearing/tear-out strength at a bolt hole, and the deformation-considered form?

$R_n = 1.2\,l_c\,t\,F_u \leq 2.4\,d\,t\,F_u$ per bolt, where $l_c$ is the clear distance to the next hole/edge, $t$ the ply thickness, $d$ the bolt diameter. The $2.4 d t F_u$ cap limits hole elongation; $\phi = 0.75$.

What is the nominal strength of a fillet weld (AISC), and the resulting strength per inch for a $\tfrac{1}{16}$ in of weld leg using E70 electrodes?

$R_n = F_{nw} A_{we} = 0.60 F_{EXX}\,(0.707 w)\,L$, with $\phi = 0.75$. For E70, this gives a design strength of $\approx 1.392$ kips per inch per sixteenth of an inch of leg size.

In NDS sawn lumber design (ASD), what is the general form of an adjusted allowable design value?

Adjusted value = reference design value $\times$ product of adjustment factors, e.g. $$F'_b = F_b\,C_D\,C_M\,C_t\,C_L\,C_F\,C_{fu}\,C_i\,C_r.$$ Each $C$ accounts for load duration, moisture, temperature, stability, size, etc.

What does the NDS load duration factor $C_D$ adjust, and give representative values.

$C_D$ adjusts allowable stress (ASD) for the cumulative duration of the maximum load. Representative values: permanent $0.9$; ten-year (occupancy live) $1.0$; snow $1.15$; construction (7-day) $1.25$; wind/seismic $1.6$; impact $2.0$.

What is the NDS beam stability factor $C_L$ used for, and what reference quantity drives it?

$C_L$ reduces bending capacity for lateral-torsional instability of a bending member. It is computed from the slenderness ratio $R_B = \sqrt{\dfrac{l_e d}{b^2}}$ and the ratio $F_{bE}/F_b^*$, where $F_{bE}$ is the critical buckling design value.

How does glued-laminated timber (glulam) differ structurally from sawn lumber, and what is the volume factor $C_V$?

Glulam is built up from thin laminations bonded with adhesive, allowing larger sizes, controlled lamination grading (higher-grade outer laminations), and cambering. $C_V$ reduces bending design value for larger member volume and replaces the size factor $C_F$ (use the smaller of $C_V$ and $C_L$).

Name common engineered wood products (EWPs) and one defining characteristic of each.

LVL (laminated veneer lumber) – parallel veneers, high uniform strength; PSL (parallel strand lumber) – long strands, used for heavy beams/columns; LSL (laminated strand lumber); Glulam – bonded dimension-lumber laminations; I-joists – flange (LVL/lumber) + OSB web for floor/roof joists.

In the NDS yield-limit (European) model for a single dowel-type fastener, what governs the reference lateral design value $Z$?

$Z$ is the smallest value from the yield-limit equations representing different yield modes: Mode I (bearing in members), Mode II (rotation), Mode III (one plastic hinge + bearing), and Mode IV (two plastic hinges in the fastener). Each depends on dowel bearing strengths $F_e$, fastener diameter, and member thicknesses.

What is the NDS dowel bearing strength relationship to specific gravity, and the withdrawal design value form for a nail/screw?

Dowel bearing strength increases with specific gravity $G$ (e.g., $F_e \approx 11200\,G$ for bolts loaded parallel to grain). Nail withdrawal reference $W$ also scales with $G$; design withdrawal $= W \times$ penetration depth $\times$ adjustment factors.

For cold-formed steel (AISI), why is the effective width method used, and what is the key local-buckling slenderness parameter?

Thin cold-formed elements buckle locally before yielding, so only an 'effective width' carries stress at $f$. The slenderness factor is $$\lambda = \sqrt{\frac{f}{F_{cr}}},\quad F_{cr} = k\frac{\pi^2 E}{12(1-\mu^2)}\left(\frac{t}{w}\right)^2.$$ If $\lambda \leq 0.673$, $b = w$ (fully effective); otherwise $b = \rho w$ with $\rho = (1 - 0.22/\lambda)/\lambda$.

What additional strength benefit does cold-forming impart to cold-formed steel corners, and what limit states are unique to CFS members?

Cold work of forming raises the yield strength at corners (strain hardening). Unique/critical limit states include local buckling, distortional buckling, web crippling, and shear lag — addressed via the Effective Width or Direct Strength Method.

In wood floor/roof framing, what is the load path for gravity loads, and how is the tributary area concept applied to a typical joist?

Load path: sheathing → joists/rafters → beams/girders → columns or bearing walls → foundation. A joist carries the area equal to its span length times the tributary width (half the spacing to the adjacent joist on each side), so uniform load $w = (\text{area load}) \times (\text{joist spacing})$.

In masonry (TMS 402), how does the specified compressive strength of masonry $f'_m$ relate to the unit and the assembly, and how is it verified?

$f'_m$ is the specified strength of the completed assemblage (units + mortar + grout), not the unit alone. It is verified by the Unit Strength Method (tables relating unit strength + mortar type to $f'_m$) or by the Prism Test Method (testing built prisms).

What is the modulus of elasticity of clay and concrete masonry per TMS 402, and a typical value of $f'_m$?

For concrete masonry $E_m = 900 f'_m$; for clay masonry $E_m = 700 f'_m$. A common specified value is $f'_m = 1500\text{ to }2000$ psi for concrete masonry by the unit strength method.

For an allowable-stress-design reinforced masonry beam (TMS 402), what is the maximum allowable masonry compressive bending stress, and what design assumption is used?

$F_b = 0.45 f'_m$ for flexural compression. Design uses cracked-transformed-section (working stress) assumptions: plane sections remain plane, linear stress-strain, masonry takes no tension, and the steel-to-masonry modular ratio $n = E_s/E_m$ transforms reinforcement.

For a reinforced masonry lintel/beam, what limits the steel and what is the nominal moment by strength design (TMS 402)?

Strength design uses $\varepsilon_{mu}=0.0025$ (concrete masonry) and an equivalent stress block of $0.80 f'_m$ over depth $a = \dfrac{A_s f_y}{0.80 f'_m b}$, giving $M_n = A_s f_y\left(d - \dfrac{a}{2}\right)$, $\phi = 0.90$. Maximum reinforcement limits ensure ductile (tension-controlled) behavior.