Seismic Design of Steel, Composite, Timber, and Masonry Systems

Introduction

Earthquake-resistant design requires more than satisfying elastic strength equations. A structural system must possess a complete and dependable load path, adequate stiffness, stable hysteretic response, controlled deformation, and protection against brittle failure. These requirements are achieved differently in steel, composite, timber, reinforced masonry, and unreinforced masonry (URM) because each material has distinct cyclic characteristics.

Steel can develop substantial ductility, but local buckling, connection fracture, brace instability, and panel-zone failure may prevent it. Composite construction combines steel and concrete efficiently, although cyclic force transfer through slabs, shear connectors, diaphragms, and joints requires careful treatment. Timber structures are lightweight and often dissipate energy through yielding fasteners rather than the wood itself. Reinforced masonry may be detailed for ductile flexure, whereas URM commonly requires evaluation and retrofit because of weak tensile resistance and poor wall-to-diaphragm anchorage.

This chapter presents material-specific design procedures while emphasizing a common seismic principle: identify the intended yielding mechanism and design all non-dissipative components for the maximum forces that the mechanism can deliver. Numerical coefficients, resistance factors, permitted systems, and detailing limits must be taken from the governing standard.

Learning Objectives

After completing this chapter, the reader should be able to:

1. Select suitable steel moment-frame and braced-frame mechanisms.

2. calculate capacity-design actions in beams, columns, braces, and connections;

3. evaluate composite members and cyclic force transfer at steel–concrete interfaces;

4. design timber diaphragms, shear walls, chords, collectors, and connections;

5. construct axial force–moment interaction relationships for reinforced masonry;

6. evaluate in-plane and out-of-plane URM mechanisms quantitatively; and

7. develop coordinated retrofit strategies for mixed-material buildings.

1. Material-Specific Seismic Behaviour

1.1 Strength, stiffness, and deformation capacity

Seismic design distinguishes between:

• required strength, obtained from the prescribed analysis and load combinations;
• design strength, equal to the nominal resistance multiplied by the applicable resistance factor;
• expected strength, an estimate of actual strength including material overstrength; and
• deformation capacity, the rotation, strain, slip, or drift that can be sustained before unacceptable degradation.

The intended response is usually organized through a hierarchy of resistance:

\[

R_{protected}>R_{demand\ from\ probable\ yielding}

\]

Protected components include collectors, connections, columns, brace gussets outside designated yield regions, diaphragm anchors, and foundations. Their demand is not necessarily the elastic analysis force; it may be the force generated when dissipative components reach probable or expected resistance.

1.2 Cyclic failure modes

Steel frames may experience local buckling, low-cycle fatigue, bolt slip, weld fracture, panel-zone yielding, or brace buckling. Composite members are also affected by slab cracking, stud fatigue, concrete crushing, and reinforcement fracture. Timber systems can fail through fastener yielding, nail withdrawal, splitting, rolling shear, crushing, or brittle net-section rupture. Masonry failures include flexural rocking, sliding, diagonal tension, toe crushing, bar fracture, lap-splice failure, and out-of-plane instability.

A design is ductile only when brittle modes are demonstrably stronger than the intended yielding mode.

2. Steel Moment-Resisting Frames

2.1 Mechanism selection

A moment-resisting frame develops lateral resistance through bending of beams and columns and deformation of beam-to-column joints. A desirable mechanism generally includes beam hinging at selected locations while avoiding column sidesway mechanisms. The strong-column–weak-beam principle is assessed at each joint using probable member strengths, axial-force effects, and the requirements of the applicable standard.

The design sequence is:

1. establish drift and strength demands from structural analysis;

2. select beams for flexural strength, stability, and rotation capacity;

3. determine probable plastic moments at expected material strength;

4. derive beam shear from probable end moments and gravity loading;

5. design moment connections and panel zones for capacity-design actions;

6. check column axial-flexural interaction and joint strength; and

7. verify stability, second-order effects, and protected-zone detailing.

2.2 Beam capacity and stability

For a compact, adequately braced steel section that can attain its plastic resistance,

\[

M_n=F_yZ

\]

where \(F_y\) is specified yield stress and \(Z\) is the plastic section modulus. This expression is not applicable when local buckling, lateral-torsional buckling, holes, or other limit states reduce resistance.

A probable moment may be represented as

\[

M_{pr}=C_{pr}R_yF_yZ

\]

where \(R_y\) accounts for expected yield strength and \(C_{pr}\) represents strain hardening and related effects, as prescribed by the governing standard.

2.3 Beam shear generated by plastic hinging

When probable moments develop at both ends of the hinge-to-hinge span \(L_h\), equilibrium—not division of a single moment by a distance—controls the hinge-induced shear:

\[

V_p=\frac{M_{pr,L}+M_{pr,R}}{L_h}

\]

Here the end moments act in opposite rotational senses on the physical beam segment but contribute additively to the shear magnitude. Gravity-load shear must then be superimposed with the sign that maximizes each end demand. For a uniformly distributed factored gravity load \(w_u\) over a simply supported hinge-to-hinge segment,

\[

V_{u,L}=\frac{w_uL_h}{2}\pm V_p,\qquad

V_{u,R}=\frac{w_uL_h}{2}\mp V_p

\]

This gravity expression is a special symmetric case. For unequal spans, point loads, or hinges offset from the member ends, complete free-body equilibrium is required.

Worked Example 1: Capacity-design shear in a moment-frame beam

A beam has a hinge-to-hinge distance of 5.6 m. Probable end moments are 420 and 380 kN·m. The factored gravity load over the hinge span is 24 kN/m.

Plastic-mechanism shear:

\[

V_p=\frac{420+380}{5.6}=142.9\text{ kN}

\]

Gravity reaction at either end:

\[

V_g=\frac{24(5.6)}{2}=67.2\text{ kN}

\]

The end-shear envelope is therefore

\[

V_{u,\max}=67.2+142.9=210.1\text{ kN}

\]

and the opposite-sign combination has magnitude

\[

|67.2-142.9|=75.7\text{ kN}.

\]

The beam web, connection, and adjacent force-transfer components must be checked for the appropriate directional envelope. Using \(M_{pr}/L_h\) would omit the contribution from the second plastic hinge and would be incorrect.

2.4 Moment connections and panel zones

A qualified moment connection must transmit probable beam flexure and the associated shear while sustaining the required cyclic rotation. Design checks typically include:

• flange and web weld fracture;
• bolt shear, bearing, slip, and net-section rupture;
• continuity-plate and doubler-plate requirements;
• column flange bending and web crippling;
• panel-zone shear yielding and stability;
• reduced-beam-section geometry, where used; and
• demand at weld access holes and other stress concentrations.

Connection qualification should correspond to the member sizes, materials, geometry, fabrication process, and required rotation. Extrapolation beyond tested limits requires engineering justification.

3. Steel Braced Frames

3.1 Concentrically braced frames

In concentrically braced frames, braces primarily resist axial force. Special concentrically braced frames obtain energy dissipation from brace tension yielding and post-buckling cyclic behaviour. The brace, gusset, beam, column, collector, and foundation must form a continuous load path.

Brace tensile limit states include gross-section yielding and net-section rupture. Representative nominal strengths are

\[

P_{n,y}=F_yA_g,\qquad P_{n,r}=F_uA_e

\]

where \(A_g\) is gross area and \(A_e\) is effective net area. Governing standards apply resistance factors and may require expected strengths \(R_yF_yA_g\) or \(R_tF_uA_e\) for capacity design.

Compression resistance must be obtained from the applicable column curve, accounting for slenderness \(KL/r\), local slenderness, and expected post-buckling behaviour. Beams, columns, gussets, and connections are designed for the force combination associated with expected brace tension and prescribed compression resistance, not merely analysis-level brace forces.

Gusset plates require checks for bolt or weld resistance, Whitmore-section yielding and buckling, block shear, edge tear-out, and out-of-plane rotational accommodation. A gusset that is strong but rotationally restrained can precipitate brace fracture near its end.

3.2 Eccentrically braced frames

An eccentrically braced frame contains a deliberately selected link that yields in shear, flexure, or a combination of both. Link length controls the mechanism. Short links are shear dominated; long links are flexure dominated. Link webs, stiffeners, lateral bracing, and link-to-column connections must satisfy stringent cyclic requirements. Braces, columns, and connections outside the link are protected using the link’s expected overstrength.

3.3 Buckling-restrained braced frames

A buckling-restrained brace has a yielding steel core restrained against global buckling by a casing. It produces comparatively stable tension and compression hysteresis, although compression strength may exceed tension strength because of friction and confinement. The frame, gussets, collectors, and foundations must be designed for adjusted brace strengths established by qualification testing.

4. Composite Steel–Concrete Systems

4.1 Composite resistance

Composite floors combine a steel beam with a concrete slab through mechanical shear connectors. In positive flexure, slab compression and steel tension can form an efficient internal couple. If the plastic neutral axis lies in the slab and the steel tension resultant is \(T\), equilibrium gives

\[

C=T=0.85f'_cb_{eff}a

\]

and therefore

\[

a=\frac{T}{0.85f'_cb_{eff}}.

\]

If \(d\) is measured from the slab top to the steel tension resultant, the nominal moment is

\[

M_n=T\left(d-\frac{a}{2}\right).

\]

The expression is valid only for the stated geometry and assumed stress block. No additional slab-thickness term may be added when \(d\) is already measured from the slab top.

Worked Example 2: Positive composite flexural resistance

A composite beam has a steel tensile area of 6000 mm² with \(F_y=345\) MPa. The effective slab width is 1800 mm, \(f'_c=30\) MPa, slab thickness is 130 mm, and the distance from slab top to the steel tension resultant is 330 mm. Assume full tensile yielding and that the compression block remains in the slab.

\[

T=A_sF_y=6000(345)=2.070\times10^6\text{ N}=2070\text{ kN}

\]

\[

a=\frac{2.070\times10^6}{0.85(30)(1800)}=45.1\text{ mm}<130\text{ mm}

\]

Thus the assumed neutral-axis location is consistent. The lever arm is

\[

z=330-\frac{45.1}{2}=307.45\text{ mm}.

\]

Hence

\[

M_n=2070(0.30745)=636.4\text{ kN·m}.

\]

If each shear connector has a design resistance of 90 kN, at least

\[

n=\left\lceil\frac{2070}{90}\right\rceil=23

\]

connectors are required to transfer the full longitudinal force over the relevant shear span, subject to spacing, fatigue, deck-orientation, and seismic detailing requirements.

4.2 Composite cyclic connections

Monotonic composite strength does not guarantee cyclic performance. At moment-frame joints, the slab may increase positive flexural strength, shift the neutral axis, and enlarge column and panel-zone demands. Under moment reversal, slab cracking reduces stiffness and forces reinforcement and steel components to transfer tension.

A cyclic connection design should therefore:

1. determine positive and negative probable beam strengths, including slab reinforcement where effective;

2. derive connection and panel-zone forces from the larger directional demand;

3. provide reinforcement crossing the joint or collector interface;

4. check stud demand between the point of zero longitudinal force and the critical section;

5. avoid placing vulnerable stud groups or abrupt deck discontinuities in designated plastic-hinge zones;

6. check concrete crushing, splitting, reinforcement development, weld fracture, and low-cycle fatigue; and

7. use a connection qualified for the required cyclic rotation.

If a probable slab compression force is 900 kN and the design resistance of each effective stud is 75 kN, at least 12 studs are required by strength. This count does not replace checks for cyclic degradation, spacing, group effects, or concrete breakout.

Composite columns and walls require axial force–bending interaction, confinement, local buckling, load-transfer, and fire-protection checks. During seismic response, load sharing cannot be assigned arbitrarily; compatibility and interface transfer must be demonstrated.

5. Timber Seismic Systems

5.1 Ductility through connections

Wood is strong relative to its mass, but many wood failure modes are brittle. Timber seismic systems consequently dissipate energy mainly through yielding dowel-type fasteners, nails, screws, straps, and proprietary devices. Capacity design should promote fastener yielding while preventing splitting, plug shear, row tear-out, net-section rupture, and brittle anchor failure.

Moisture, grain direction, cyclic withdrawal, construction tolerances, corrosion, and duration-of-load rules affect resistance. Values must be taken from the governing timber and seismic standards.

5.2 Diaphragm design

A timber diaphragm distributes inertial forces to vertical resisting elements. Design steps are:

1. establish diaphragm forces, including amplification required for collectors and their connections;

2. determine diaphragm shear and classify flexibility using the governing standard;

3. design sheathing and edge fastening for unit shear;

4. calculate chord forces from diaphragm bending;

5. design collectors and drag struts for axial transfer; and

6. verify openings, re-entrant corners, splices, anchorage, and deflection.

For a diaphragm idealized as a simply supported deep beam of depth \(d_D\), the chord force at a section may be estimated by

\[

T_c=\frac{M_D}{d_D},

\]

where \(M_D\) is diaphragm bending moment. The relation assumes a chord couple separated by \(d_D\); local discontinuities require more detailed analysis.

5.3 Timber shear walls

For a wall line with available sheathed length \(L_w\) and design unit shear resistance \(v_d\),

\[

V_d=v_dL_w,

\]

provided aspect-ratio, anchorage, panel-edge, and opening requirements are satisfied.

Overturning is transferred by end posts and hold-downs. For a wall of length \(L_w\) subjected to overturning moment \(M_{ot}\), the idealized end-force couple is

\[

T_{hd}=\frac{M_{ot}}{L_w}.

\]

Net hold-down demand may be reduced only by reliably present stabilizing gravity load under the governing load combination. Anchorage must also be checked for steel yielding, wood crushing or splitting, concrete breakout, and foundation transfer.

Worked Example 3: Timber wall strength and hold-down demand

A 4.8 m long, 3.0 m high timber shear wall resists a storey shear of 72 kN. Its permitted design unit shear is 15 kN/m. Ten kilonewtons of reliable stabilizing dead-load reaction acts at the tension end.

Shear resistance:

\[

V_d=15(4.8)=72\text{ kN}.

\]

The wall just satisfies the required shear strength, although drift and detailing still require verification. Base overturning moment is

\[

M_{ot}=72(3.0)=216\text{ kN·m}.

\]

Idealized tension force:

\[

T_{hd}=\frac{216}{4.8}=45\text{ kN}.

\]

After the permitted stabilizing reaction,

\[

T_{net}=45-10=35\text{ kN}.

\]

The hold-down assembly and its load path require at least the factored design resistance corresponding to 35 kN, subject to any code-required overstrength or amplification.

Wall drift includes sheathing shear deformation, fastener slip, chord or stud axial deformation, and hold-down elongation. Relying only on panel shear stiffness can substantially underestimate drift.

5.4 Mass timber systems

Cross-laminated timber and other mass-timber systems can use rocking walls, replaceable steel fuses, post-tensioning, or conventional shear connections. Their performance depends on connection cyclic response, panel rocking, floor-to-wall transfer, rolling shear, fire design, and residual deformation. Proprietary components require qualification data consistent with expected cyclic displacement and environmental conditions.

6. Reinforced Masonry

6.1 Flexural design and axial-force interaction

Reinforced masonry walls can develop ductile flexural response when vertical reinforcement yields before diagonal shear failure, toe crushing, splice failure, or bar buckling. Axial load changes both flexural strength and deformation capacity: moderate compression can increase strength, while high compression accelerates crushing and reduces ductility.

An axial force–moment interaction diagram is generated using strain compatibility:

1. assume a neutral-axis depth \(c\);

2. impose a linear strain distribution and the prescribed ultimate masonry strain;

3. calculate reinforcement strains and stresses, limited by material laws;

4. integrate masonry compression using the code-approved stress block;

5. enforce axial equilibrium; and

6. calculate moment about a consistent reference axis.

For a simplified rectangular compression block,

\[

P_n=C_m+\sum C_s-\sum T_s,

\]

\[

M_n=\sum F_i z_i,

\]

where \(F_i\) are internal masonry and steel resultants and \(z_i\) are their distances from the section centroid. Applicable strength-reduction factors and minimum eccentricity rules must then be applied.

Worked Example 4: Simplified masonry interaction point

Consider a 3.0 m long, 200 mm thick wall with \(f'_m=15\) MPa. Tension reinforcement of 1200 mm² is located 2.7 m from the compression edge and yields at 420 MPa. At a nominal axial compression of 300 kN, use an illustrative compression stress of \(0.8f'_m\). Ignore compression reinforcement for this demonstration.

Steel tension:

\[

T=1200(420)=504\text{ kN}.

\]

Axial equilibrium requires

\[

C_m=P_n+T=300+504=804\text{ kN}.

\]

Compression-block depth:

\[

a=\frac{804000}{0.8(15)(200)}=335\text{ mm}.

\]

Taking moments about the section centroid,

\[

M_n=C_m\left(1.5-\frac{0.335}{2}\right)+T(2.7-1.5)

\]

\[

M_n=804(1.3325)+504(1.2)=1676\text{ kN·m approximately}.

\]

This is one nominal interaction point, not a complete design capacity. Steel yielding must be verified from strain compatibility, and code-specific stress-block parameters, resistance factors, confinement limits, and slenderness effects must be applied.

6.2 Shear and capacity design

Wall shear demand should include the force associated with probable flexural strength, where required, because a wall stronger in flexure than assumed can deliver larger shear to its web, collectors, and foundation. Masonry shear resistance may contain masonry and reinforcement contributions, but permitted expressions and upper limits are code-specific. The design must check diagonal tension, sliding at construction joints, web crushing, boundary compression, reinforcement anchorage, and foundation transfer.

Lap splices and couplers should be kept away from critical plastic regions unless qualified for the expected inelastic strain. Boundary reinforcement and transverse restraint may be required where compression strains are high.

7. Unreinforced Masonry Evaluation and Retrofit

7.1 Evaluation philosophy

URM should generally be evaluated rather than assumed to possess reinforced-masonry ductility. A defensible assessment includes material testing, wall geometry, bond pattern, diaphragm flexibility, anchorage, prior damage, alterations, foundation condition, and interaction between orthogonal walls.

Capacity is governed by the weakest credible mechanism. Increasing in-plane strength without correcting out-of-plane instability or poor anchorage may worsen overall risk.

7.2 In-plane mechanisms

For a pier of width \(b\), height \(h\), and axial compression \(N\), a simple no-tension rocking estimate gives

\[

M_r\approx N\frac{b}{2},\qquad V_r\approx\frac{Nb}{2h}.

\]

This is an incipient-rocking idealization that neglects compression-block depth, tensile bond, distributed self-weight effects, and vertical acceleration. More refined equilibrium is needed after rocking begins.

Sliding resistance may be represented conceptually by

\[

V_s=\mu N+V_c,

\]

where \(\mu\) is an interface friction coefficient and \(V_c\) is any code-permitted cohesive contribution. Cohesion should not be credited where cracking, deterioration, or cyclic degradation makes it unreliable.

Diagonal-tension resistance is normally evaluated using empirically calibrated standard provisions. It must not be inferred from rocking or sliding equations. The governing capacity is the minimum credible resistance among rocking, sliding, diagonal tension, toe crushing, and connection failure.

7.3 Out-of-plane mechanisms

Out-of-plane failure may involve a one-way wall strip, vertical cantilever, parapet, arching segment, or multi-block rocking mechanism. Boundary conditions must reflect actual anchorage rather than assumed fixity.

For a uniform free-standing parapet of height \(h\), thickness \(t\), and weight \(W\), incipient overturning under horizontal acceleration \(a\) follows

\[

W\frac{t}{2}=\frac{W}{g}a\frac{h}{2}.

\]

Thus

\[

\frac{a_c}{g}=\frac{t}{h}.

\]

This special-case rigid-block expression neglects mortar tension, vertical acceleration, degradation, and dynamic rocking effects.

Worked Example 5: URM parapet screening

A free-standing URM parapet is 1.8 m high and 240 mm thick. Assuming rigid-block overturning,

\[

\frac{a_c}{g}=\frac{0.24}{1.8}=0.133.

\]

The nominal initiation acceleration is only 0.133g. If the applicable out-of-plane demand exceeds this value, stabilization is required. A practical retrofit may include steel braces or anchors connected to a competent diaphragm, but the wall, anchor, diaphragm, collector, and supporting elements must all be verified.

7.4 Retrofit techniques

Possible interventions include wall-to-diaphragm anchors, parapet bracing, diaphragm strengthening, collector installation, reinforced overlays, shotcrete, grout injection, localized reconstruction, steel frames, and fibre-reinforced systems. Compatibility, reversibility in heritage structures, corrosion, moisture trapping, fire performance, and foundation demand must be considered.

Anchor design requires checks for steel resistance, pull-out, masonry breakout, edge distance, group effects, cyclic degradation, and connection to the diaphragm. Proof testing may support quality assurance but should follow a statistically defensible sampling plan.

8. Illustrative Integrated Case Study: Retrofit of a Mixed-Material Warehouse

Background

This fictional case concerns a two-storey warehouse with timber roof diaphragms, URM perimeter walls, and lightly connected steel gravity framing. The building has flexible diaphragms, unbraced parapets, and inadequate wall anchorage.

Problem

Analysis identifies a roof diaphragm shear of 360 kN. The diaphragm distributes this force to two proposed steel braced bays, nominally 180 kN each. The 12 m deep diaphragm develops a maximum bending moment of 1080 kN·m. Existing parapets are 1.5 m high and 200 mm thick.

Analysis

The required diaphragm chord force is

\[

T_c=\frac{1080}{12}=90\text{ kN}.

\]

Chord splices and end connections must therefore transfer at least the governing amplified design force, not merely the force in individual sheathing fasteners.

Parapet screening gives

\[

a_c/g=0.20/1.50=0.133.

\]

This low capacity confirms the need for stabilization. The existing URM walls cannot be relied upon as ductile seismic elements without detailed verification.

Approach and solution

The retrofit strategy includes:

• new steel buckling-restrained braced bays with qualified braces;
• timber diaphragm edge nailing and blocked panel joints;
• steel chord and collector elements designed for amplified transfer forces;
• distributed wall anchors with verified masonry breakout resistance;
• parapet braces connected into roof framing rather than sheathing alone; and
• local wall repairs and removal of unstable masonry.

Brace connection and foundation demands are based on adjusted brace strengths. Collector splices are kept away from abrupt diaphragm discontinuities. Installation specifications require anchor proof testing, weld inspection, fastener verification, and documentation of concealed work.

Outcome

The intervention establishes an explicit load path from roof mass through sheathing, chords, collectors, braced frames, and foundations. URM walls are stabilized out of plane but are not assigned unverified ductile in-plane resistance.

Learning points

A successful retrofit is controlled by interfaces. Strengthening only the braced frames would not correct diaphragm, collector, parapet, or anchorage vulnerabilities. Capacity design must extend across material boundaries.

9. Professional Practice, Regulation, and Emerging Methods

Designers must use the legally adopted loading, steel, concrete, timber, masonry, welding, and assessment standards. System ductility factors, drift limits, resistance factors, expected-strength coefficients, and permitted configurations are jurisdiction-specific and should never be combined selectively from incompatible codes.

Existing-building assessment requires transparent assumptions and documentation of uncertainty. Ethical practice prohibits assigning favourable material strengths or boundary conditions without evidence. Heritage significance, occupancy during construction, disproportionate-collapse risk, and nonstructural hazards should be included in decision-making.

Nonlinear analysis can improve understanding of hinge rotations, brace cycles, wall rocking, and connection demands, but results depend on constitutive models and deterioration rules. Artificial intelligence can assist with drawing review, damage-image classification, and model checking; it cannot replace site investigation, engineering judgment, or code verification. Digital fabrication, replaceable fuses, self-centering systems, mass-timber rocking walls, and performance-based assessment are important contemporary developments.

10. Best-Practice Design Checklist

1. Define the intended yielding mechanism before sizing protected components.

2. Derive capacity-design actions from complete free-body equilibrium.

3. Include expected material strength, strain hardening, and directional asymmetry.

4. Verify both force resistance and cyclic deformation capacity.

5. Treat diaphragms, collectors, anchors, joints, and foundations as part of the seismic system.

6. Prevent brittle timber and masonry failure modes through connection hierarchy.

7. Evaluate URM in-plane and out-of-plane mechanisms separately.

8. Check positive and negative composite strengths, including slab participation.

9. Confirm that analytical boundary conditions exist in the constructed building.

10. Specify inspection, testing, tolerances, and acceptance criteria.

Chapter Summary

Seismic design across steel, composite, timber, and masonry systems is governed by mechanism control and reliable force transfer. Steel moment frames require probable-moment equilibrium, qualified connections, stable members, and protected columns and panel zones. Braced frames require braces or links to dissipate energy while connections, collectors, and foundations remain protected.

Composite resistance depends on consistent geometry, longitudinal shear transfer, and cyclic treatment of slabs, reinforcement, studs, and joints. Timber systems derive much of their ductility from fastener yielding; brittle wood failures, hold-down flexibility, and diaphragm discontinuities must be controlled. Reinforced masonry requires axial force–moment interaction and capacity-protected shear behaviour. URM must be assessed mechanism by mechanism, especially for deficient out-of-plane anchorage. In mixed-material structures, interfaces commonly govern performance.

Key Terms

Capacity design: Design of protected components for forces generated by probable yielding of dissipative components.

Collector: An element that transfers diaphragm forces to vertical seismic-resisting elements.

Composite action: Force transfer that enables different materials to resist load as an integrated section.

Cyclic degradation: Reduction of strength or stiffness under repeated reversed deformation.

Diaphragm chord: Tension or compression element resisting diaphragm bending.

Ductility: Ability to undergo substantial inelastic deformation before loss of resistance.

Expected strength: Estimated actual material or component strength including overstrength.

Gusset plate: Plate connecting a brace to beams, columns, or other framing.

Hold-down: Anchorage device resisting overturning tension at a timber wall boundary.

Interaction diagram: Relationship between axial-force and moment resistance.

Link: Designated yielding segment in an eccentrically braced frame.

Panel zone: Column-web region enclosed by beam and column flanges at a moment joint.

Plastic hinge: Localized region undergoing significant inelastic rotation.

Probable moment: Expected flexural strength used to derive capacity-design actions.

Protected zone: Region in which attachments or discontinuities are restricted to preserve cyclic performance.

Rocking: Rotation of a wall or block caused by opening at its base or joints.

Shear connector: Device transferring longitudinal shear across a composite interface.

Unreinforced masonry: Masonry without reinforcement adequate to satisfy reinforced-masonry requirements.

Whitmore section: Effective gusset width used for selected yielding and buckling checks.

Review Questions

Short Answer Questions

1. Why are expected strengths used when designing protected seismic components?

2. How is beam shear obtained from probable moments at two plastic hinges?

3. What is the principal source of ductility in conventional timber shear walls?

4. Why can slab participation increase moment-frame joint demand?

5. Name three credible in-plane failure mechanisms for URM walls.

Long Answer Questions

1. Explain the complete capacity-design procedure for a steel moment-resisting frame.

2. Compare concentrically braced, eccentrically braced, and buckling-restrained braced frames.

3. Discuss the design and detailing requirements for cyclic composite beam-to-column connections.

4. Develop a design procedure for a timber diaphragm, including chords, collectors, and anchorage.

5. Explain how an axial force–moment interaction diagram is constructed for reinforced masonry.

Analytical / Application Questions

1. A beam has probable end moments of 500 and 440 kN·m over a 6.0 m hinge span and carries 20 kN/m factored gravity load. Determine its maximum end-shear demand.

2. Evaluate the overturning initiation acceleration of a 2.0 m high, 250 mm thick free-standing URM parapet and recommend an appropriate retrofit concept.

3. Develop a capacity-design load path for a timber diaphragm connected to steel braced frames within a URM building, identifying all protected interfaces.

Multiple Choice Questions with Answers

Question 1

A beam has probable end moments of 420 kN·m and 380 kN·m over a 5.0 m hinge-to-hinge span. What is the hinge-induced shear magnitude?

A. 76 kN

B. 84 kN

C. 160 kN

D. 200 kN

Correct Answer: C. 160 kN

Question 2

In the composite flexure expression where d is measured from the slab top to the steel tension resultant, what is the correct lever arm for a compression-block depth a?

A. d − a/2

B. d + a/2

C. d + tc/2 − a/2

D. d − tc/2

Correct Answer: A. d − a/2

Question 3

Which component is intended to dissipate energy in a special concentrically braced frame?

A. Gravity column base plate

B. Brace through tension yielding and cyclic buckling

C. Floor slab compression block only

D. Foundation soil exclusively

Correct Answer: B. Brace through tension yielding and cyclic buckling

Question 4

What is the designated yielding component in an eccentrically braced frame?

A. Diaphragm chord

B. Column splice

C. Link

D. Foundation tie

Correct Answer: C. Link

Question 5

A 4.5 m long timber wall carries a 90 kN storey shear at a height of 3.0 m. Ignoring stabilizing gravity load, what is the idealized hold-down tension?

A. 30 kN

B. 45 kN

C. 60 kN

D. 270 kN

Correct Answer: C. 60 kN

Question 6

For a free-standing rigid URM parapet 1.5 m high and 0.225 m thick, what is the idealized overturning initiation acceleration?

A. 0.075g

B. 0.150g

C. 0.225g

D. 0.300g

Correct Answer: B. 0.150g

Question 7

Which method is appropriate for developing reinforced-masonry axial force–moment interaction?

A. Strain compatibility and internal-force equilibrium

B. Dividing shear strength by wall height

C. Assuming zero axial-force influence

D. Using timber fastener yield equations

Correct Answer: A. Strain compatibility and internal-force equilibrium

Question 8

When evaluating an unreinforced masonry pier, the governing in-plane resistance should be based on which principle?

A. Use rocking resistance in every case

B. Use the largest calculated mechanism resistance

C. Use the minimum credible resistance among applicable failure mechanisms

D. Ignore sliding where axial compression exists

Correct Answer: C. Use the minimum credible resistance among applicable failure mechanisms

Question 9

Why must positive and negative probable strengths both be considered in composite moment connections?

A. Concrete and reinforcement participation changes under moment reversal

B. Steel has no tensile strength under negative bending

C. Shear connectors eliminate all cyclic effects

D. The slab remains uncracked in both directions

Correct Answer: A. Concrete and reinforcement participation changes under moment reversal

Question 10

Which statement best describes capacity design?

A. All components are designed to yield simultaneously

B. Protected components are designed for forces generated by the probable yielding mechanism

C. Elastic analysis forces are always used without amplification

D. Connections are intentionally made weaker than brittle members

Correct Answer: B. Protected components are designed for forces generated by the probable yielding mechanism