Structural Engineering Exam (SE) Lateral Forces — Bridges Depth Syllabus

Distinguish a force-based versus displacement-based assessment of bridge column seismic adequacy.

Force-based design checks that member force demands (reduced by $R$) are below capacities. Displacement-based design checks that the displacement capacity $\Delta_c$ (from pushover, limited by plastic rotation) exceeds the displacement demand $\Delta_d$ from the response spectrum: $\Delta_c \geq \Delta_d$. Higher SDCs require the displacement check.

How is the seismic behavior of a pile foundation idealized for analysis, and what is the 'point of fixity' concept?

Laterally loaded piles are modeled with soil springs (p-y curves) or as a cantilever fixed at an equivalent depth — the point of fixity — below which the pile is assumed rigidly restrained. The depth to fixity (often $\sim$5–10 pile diameters) sets the effective cantilever length for stiffness and plastic-hinge demand.

What is a p-y curve and what does it represent in pile seismic analysis?

A p-y curve is a nonlinear relationship between soil resistance per unit length ($p$) and lateral pile deflection ($y$) at a given depth. It captures soil stiffness and ultimate resistance, modeling soil-structure interaction so the pile's lateral load-deflection and bending behavior under seismic loads can be computed.

In capacity-protected pile/foundation design, should plastic hinges be allowed in piles, and what is the preferred philosophy?

Generally foundations are capacity-protected to remain essentially elastic (hinging confined to columns), because buried/underwater pile damage is hard to inspect and repair. Where in-ground hinging is unavoidable (e.g., pile-bent structures), the hinge must be detailed for ductility and its location/limited damage explicitly accepted in design.

What is liquefaction and why is it a critical seismic hazard for bridge foundations?

Liquefaction is the loss of shear strength and stiffness in saturated, loose, cohesionless soil when cyclic shaking raises pore pressure until effective stress approaches zero. For bridges it causes loss of pile lateral/vertical support, lateral spreading, settlement, and downdrag, potentially leading to foundation failure or span unseating.

How can abutments participate in resisting longitudinal seismic forces, and what is the benefit?

In integral or seat-type abutments, the backfill soil mobilizes passive earth pressure as the superstructure pushes into the embankment, providing significant longitudinal stiffness and force resistance. This 'abutment participation' reduces displacement and force demands on the interior columns when properly accounted for.

Write the expression for the passive earth pressure resistance available at a bridge abutment backwall.

$$P_p = \tfrac{1}{2}\,\gamma\,H^{2}\,K_p\,w$$ where $\gamma$ is the backfill unit weight, $H$ is the backwall height, $w$ is the wall width, and $K_p$ is the passive earth pressure coefficient. AASHTO often caps the mobilized passive pressure (e.g., $\sim$5 ksf per unit area for compacted backfill) scaled by displacement.

In bridge seismic models, why is abutment longitudinal stiffness often modeled as bilinear/displacement-dependent?

Passive soil resistance does not fully mobilize until the wall displaces a fraction of its height (roughly $0.01H$ to $0.05H$). So stiffness is high initially then yields at the passive capacity. A bilinear spring captures the gap-closing, mobilization, and plateau, preventing overestimation of abutment restraint at small displacements.

State the capacity design principle for a bridge bent cap (joint) relative to the column it supports.

The cap beam and beam-column joint must be designed for the column overstrength moment $M_{po}$ and the associated shear, so they remain essentially elastic and force plastic hinging into the column. The joint must transfer these forces without diagonal shear failure or bar anchorage failure.

What design forces govern a spread/pile footing under a ductile column in capacity design?

The footing is designed for the column overstrength actions: moment $M_{po}$, the corresponding shear $V_{po}$, and axial load. It is proportioned to remain elastic (no flexural or shear hinging) so that inelastic action stays in the column, checking one-way shear, punching shear, and pile/soil reactions against these capacity demands.

Contrast a fixed (monolithic/integral) column-to-superstructure connection with a pinned connection in seismic capacity design.

A fixed connection develops plastic hinges at both column ends (double curvature), doubling moment demand sharing but enabling frame action and lower drift. A pinned connection forms a single hinge at the base (single curvature), simplifying force flow and capacity protection of the cap but giving a more flexible, higher-displacement system.

What are the principal functions of bridge bearings under seismic demand?

Bearings transfer vertical and horizontal loads between superstructure and substructure while accommodating thermal/rotational movements. Under seismic demand they must either transmit lateral forces into the substructure (fixed bearings) or permit displacement while limiting it (expansion/sliding bearings), and their failure can dictate the load path.

Why are elastomeric bearings sometimes treated as a fuse or isolation element under seismic load?

Elastomeric (and lead-rubber) bearings are laterally flexible, so they lengthen the structure's period and may slip or deform, limiting the force transmitted to the substructure. This period shift moves response toward lower spectral accelerations, acting as partial isolation; design must then ensure bearing displacement capacity is sufficient.

What seismic demand must shear keys and bearing anchor bolts be designed for in a capacity-protected bridge?

They must be designed either to transmit the column overstrength capacity force into the substructure (if intended to remain intact) or to act as sacrificial fuses with a defined failure force, after which a secondary load path (e.g., shear keys, abutment) engages. The design must be internally consistent about which elements fuse.

What is the purpose of seismic restrainers (cables/rods) at bridge expansion joints and in-span hinges?

Restrainers limit the relative longitudinal movement between adjacent frames or spans during shaking, preventing the displacement from exceeding the available seat width and causing unseating/span collapse. They engage in tension after a set slack/gap is taken up, tying frames together as a backup to seat width.

What are shear keys, and what two functions can they serve at bridge abutments and bents?

Shear keys are concrete or steel blocks that restrain transverse movement of the superstructure. They can be (1) capacity-protected to transfer transverse seismic force into the substructure, or (2) sacrificial 'fuses' designed to break at a known force to protect the foundation/wingwalls, after which larger displacement is accepted.

Write a typical AASHTO minimum support (seat) length requirement $N$ for bridge bearing seats.

$$N = (8 + 0.02L + 0.08H)\,(1 + 0.000125 S^{2})$$ (inches), where $L$ is the span length to the adjacent expansion joint (ft), $H$ is the average column/pier height (ft), and $S$ is the skew angle (degrees). This empirical seat width guards against unseating from differential displacement.

Why does bridge skew increase the risk of span unseating, and how is it reflected in seat-width rules?

On skewed bridges, seismic response tends to rotate the superstructure in plan (it 'walks' off the bearings) and concentrates movement at acute corners, increasing relative displacement at the seat. The seat-width formula includes a skew amplification term $(1 + 0.000125\,S^{2})$ to require longer seats as skew $S$ grows.

How do expansion joints behave under longitudinal seismic loading, and what hazard do they create?

Expansion joints (and in-span hinges) provide a gap that opens and closes during shaking; pounding occurs when the gap closes and adjacent frames impact. They interrupt continuity of the load path, allow out-of-phase frame movement, and are the locations where unseating is most likely without adequate seat width or restrainers.

What is seismic pounding between bridge frames, and what governs its severity?

Pounding is the impact between adjacent decks/frames at expansion joints when the closing gap is exhausted. Severity grows with out-of-phase vibration (large period differences between frames), small initial gaps, and high relative velocity. It produces localized impact forces and can damage joints and bearings; balanced frame stiffness mitigates it.

Explain the principle of seismic base isolation as applied to bridges.

Isolation inserts flexible, low-lateral-stiffness devices (e.g., lead-rubber or friction-pendulum bearings) between superstructure and substructure to lengthen the fundamental period away from the high-energy region of the spectrum, reducing acceleration/force demand. Added damping controls the resulting displacement. Inelastic demand on the substructure is greatly reduced.

How does a lead-rubber bearing (LRB) dissipate seismic energy?

The rubber provides re-centering elastic stiffness and lateral flexibility, while the lead core yields in shear under cyclic displacement, providing hysteretic energy dissipation (a stable bilinear hysteresis loop). This combination gives isolation (period shift) plus damping in a single device.

For a friction-pendulum bearing, write the restoring stiffness and note how period is set.

The horizontal restoring stiffness is $$k = \frac{W}{R}$$ where $W$ is the supported weight and $R$ is the radius of the sliding concave surface. The isolated period $T = 2\pi\sqrt{R/g}$ depends only on $R$ (not mass), and friction provides the energy dissipation.

Write the design wind pressure equation form used for bridge superstructures and define its terms.

$$P_z = 2.56\times10^{-6}\,V^{2}\,K_z\,G\,C_d$$ (ksf), where $V$ is the design 3-second gust wind speed (mph), $K_z$ is the height/exposure pressure coefficient, $G$ is the gust effect factor, and $C_d$ is the drag coefficient that depends on the superstructure shape (width-to-depth ratio).

How does wind load on a bridge substructure (pier) differ in treatment from wind on the superstructure?

Wind on the substructure is applied directly as pressure on the exposed pier surfaces (using the projected area and a drag coefficient), acting simultaneously with the superstructure wind that is transferred down through bearings. Both transverse and longitudinal wind components, plus wind on live load, are combined per the load combination.

What is the difference between wind load on the structure (WS) and wind on live load (WL) in bridge design?

WS is the wind pressure acting on the exposed bridge structure itself (super- and substructure). WL is the additional wind force acting on vehicles on the deck, transmitted to the structure through the deck; it is applied as a line load along the deck and combined with WS at reduced magnitude in the strength/service combinations.

Define flutter and vortex-induced vibration as aerodynamic concerns for long-span bridges.

Flutter is a self-excited, divergent aeroelastic instability where aerodynamic forces couple with torsional/vertical motion and feed energy into the structure above a critical wind speed (catastrophic, e.g., Tacoma Narrows). Vortex-induced vibration is resonant oscillation when periodic vortex shedding locks in near a natural frequency, causing limited-amplitude fatigue-inducing motion.

Write the Strouhal relation for the vortex-shedding frequency and explain lock-in.

$$f_s = \frac{St\,V}{D}$$ where $f_s$ is the shedding frequency, $St$ is the Strouhal number, $V$ is wind speed, and $D$ is the across-wind dimension. Lock-in occurs when $f_s$ approaches a natural frequency $f_n$, and the shedding synchronizes with the structural motion, amplifying response.

How is vessel (ship/barge) collision load characterized for bridge piers, and what governs its magnitude?

Vessel collision is an extreme-event load whose design force depends on the vessel deadweight tonnage (DWT), impact velocity, and an annual frequency-of-collapse (AF) risk analysis. The equivalent static barge impact force scales roughly as $$P_B = f(\sqrt{DWT}, V)$$ with piers in the navigable channel designed or protected for the resulting force.

In AASHTO load combinations, how are extreme events such as earthquake (EQ) and vessel collision (CV) treated relative to one another?

Extreme Event I (EQ) and Extreme Event II (CV, ice, collision) are separate load combinations; extreme events are not combined with each other because their simultaneous occurrence is improbable. Each uses a live-load factor below 1.0 (e.g., $\gamma_{EQ}$ for live load in EE-I) reflecting the low probability of full live load during the event.

Describe the complete seismic lateral load path in a typical girder bridge from deck to soil.

Inertial force originates in the deck/superstructure mass → transferred through bearings (or shear keys/diaphragms) → into the bent cap → down the columns (where ductile hinging occurs) → into the footing/pile cap → through piles or footing into the foundation soil. Abutments and backfill provide a parallel longitudinal/transverse path. Each link must have adequate strength and continuity.

How are orthogonal seismic load effects combined for bridge substructure design (e.g., column biaxial demand)?

AASHTO uses the 100%–30% (or 30%–100%) directional combination: design for 100% of the response in one orthogonal direction plus 30% in the perpendicular direction, and vice versa, taking the more critical. This approximates the biaxial demand on columns since the principal earthquake direction is unknown.

Why must combined lateral effects (e.g., dead load $P$–$\Delta$) be checked alongside seismic displacement in tall bridge columns?

At large lateral displacement $\Delta$, the gravity load $P$ acting through that offset creates a secondary moment $P\Delta$ that adds to the seismic moment and can drive instability. AASHTO requires limiting this $P$–$\Delta$ effect (e.g., $P_{dl}\,\Delta_r \leq 0.25\,M_p$) so the column retains stable hysteretic capacity.