Design of Structures

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This section covers the principal load types a structure must be designed for, and how design codes combine them — using partial safety factors — to obtain the critical design load effects.

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Principal Load Types Load Type Description Dead load (DL) The permanent, self-weight of the structure and all permanently fixed elements (structural members, finishes, fixed partitions, fixed services) — essentially constant over the structure's life Imposed (live) load (LL) Variable load due to the structure's use and occupancy (people, furniture, movable equipment, stored materials); code-specified values depend on occupancy type (e.g. residential, office, assembly) Wind load (WL) Lateral (and sometimes uplift) pressure/suction exerted by wind, dependent on basic wind speed, terrain category, building height/shape, and exposure — significant for tall or light/flexible structures Snow load (SL) Load from accumulated snow on roofs, relevant in regions/elevations with significant snowfall; depends on ground snow load, roof shape/slope, and exposure Earthquake (seismic) load (EL) Inertial load induced by ground shaking during an earthquake, estimated via seismic coefficient/response spectrum methods depending on seismic zone, soil type, structure's importance, and ductility Load Combinations Since it is highly unlikely that all loads act simultaneously at their full characteristic values, design codes specify load combinations with partial safety factors applied to each load type, chosen to give an acceptably low probability of the combined design load being exceeded.

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Typical limit-state combinations (per IS 456/NBC-type codes) include:

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1.5(DL+LL), 1.2(DL+LL±WL or EL), 1.5(DL±WL or EL), and 0.9DL±1.5(WL or EL) (the last checking for possible overturning/uplift where dead load is beneficial).

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The characteristic load is the value with a defined (low) probability of being exceeded during the structure's design life; the design load is the characteristic load multiplied by the relevant partial safety factor for that load and limit state being checked.

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This section covers the materials, properties, mix design, testing, and quality control of concrete, along with the relevant Nepal (NS) and Indian (IS) codes governing concrete technology.

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Materials Material Role Cement The binder; ordinary Portland cement (OPC) and pozzolana Portland cement (PPC) are common types, characterized by grade (e.g.

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OPC 43, OPC 53) based on 28-day compressive strength Fine aggregate Sand (natural or manufactured), filling voids between coarse aggregate particles and contributing to workability, graded per specified limits (e.g. zones I–IV) Coarse aggregate Crushed stone or gravel providing bulk and strength, graded by particle size distribution; maximum size affects workability and strength Water Required for cement hydration and workability; must be free of harmful impurities (organic matter, salts, silt) that could affect strength/durability/setting Admixtures Chemical (e.g. plasticizers, retarders, accelerators, air-entraining agents) or mineral (e.g. fly ash, silica fume, GGBS) additives used to modify fresh/hardened concrete properties Properties of Concrete Workability (fresh concrete): the ease with which concrete can be mixed, transported, placed, and compacted without segregation; measured via slump test, compaction factor test, or Vee-Bee test.

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Compressive strength (hardened concrete): the principal design property, determined via standard cube (15 cm, per IS) or cylinder (per some codes) tests at 28 days; concrete is strong in compression but weak in tension (hence the need for reinforcement).

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Durability: resistance to environmental deterioration (chemical attack, freeze-thaw, corrosion of reinforcement), governed by factors including water-cement ratio, cement content, cover to reinforcement, and exposure condition.

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Mix Design A nominal mix specifies fixed proportions of cement:sand:aggregate by volume/weight (e.g.

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1:2:4) without a rigorous strength-based design procedure, typically limited to lower-grade concrete.

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A design mix is proportioned to achieve a specified target mean strength and workability using a systematic procedure (e.g.

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IS 10262 method) based on material properties, required strength, and durability requirements.

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The water-cement ratio is a critical parameter: a lower water-cement ratio generally increases strength and durability but reduces workability (Abrams' law: strength is inversely related to the water-cement ratio).

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Testing & Quality Control Fresh concrete tests: slump test (workability), compaction factor test, flow table test.

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Hardened concrete tests: compressive strength test (cube/cylinder crushed under a compression testing machine at specified curing age, typically 28 days), and non-destructive tests (e.g. rebound hammer, ultrasonic pulse velocity) for in-situ assessment.

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Quality control involves batching accuracy, proper mixing/curing, statistical control of test results (e.g. characteristic strength defined such that not more than 5% of test results fall below it), and compliance with codes (IS 456, relevant NS codes) governing materials, mix proportions, and acceptance criteria.

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This section covers the working stress and limit state methods of reinforced concrete design, and the analysis and design of RC beams and slabs for bending, shear, deflection, and bond/anchorage.

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Limit State Method Method Approach Working stress method (WSM) An older, allowable-stress-based approach: actual (service) loads are used directly, and stresses in concrete/steel are kept within specified permissible (allowable) stresses, which are fractions of the materials' ultimate strengths (a single, overall factor of safety) Limit state method (LSM) The modern, probability-informed approach used by IS 456/most current codes: structures are designed to satisfy two categories of limit states — the limit state of collapse (strength, stability) and the limit state of serviceability (deflection, cracking) — using separate partial safety factors on loads and material strengths, allowing more rational and generally more economical design Design of Beams and Slabs An under-reinforced section (less tension steel than the balanced condition) fails by yielding of steel first, giving ample warning (large deflection/cracking) before collapse — the preferred, ductile failure mode mandated by codes; an over-reinforced section fails suddenly by concrete crushing before steel yields (brittle failure), which codes seek to avoid.

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Singly reinforced beams have tension reinforcement only; doubly reinforced beams also have compression reinforcement, used when the section's dimensions are restricted and moment capacity as a singly reinforced section would be insufficient.

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One-way slabs span predominantly in one direction (supported on two opposite edges, or with length/breadth ratio > 2), designed as a beam of unit width; two-way slabs span in both directions (supported on all four edges with length/breadth ratio ≤ 2), requiring reinforcement in both directions and using moment coefficients that depend on the aspect ratio and edge (support) conditions.

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Bending, Shear, Deflection, Bond & Anchorage At the limit state of collapse in flexure, the design assumes a rectangular (or equivalent) concrete stress block at ultimate strain, plane sections remain plane, and tension is carried entirely by reinforcement (concrete's tensile strength is neglected) to determine the ultimate moment of resistance.

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Shear design checks the nominal shear stress against the concrete's design shear strength (which depends on percentage tension steel and concrete grade); where nominal shear stress exceeds this, shear reinforcement (vertical stirrups, sometimes with bent-up bars) is provided to carry the excess shear.

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Deflection control (limit state of serviceability) is commonly achieved indirectly using code-specified span- to-effective-depth ratios (modified by factors for tension/compression steel percentage and span type), avoiding a separate detailed deflection calculation in routine designs.

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Bond is the interaction (shear stress) between reinforcement and surrounding concrete that transfers force between them; adequate anchorage (development length) — the embedded length required to develop a bar's full design stress through bond — must be provided at bar ends/laps to prevent slippage/bond failure.

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This section covers the design of RC columns and isolated/combined footings, and introduces the principles of pre-stressed concrete.

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Design of Columns Columns are classified as short (where slenderness effects are negligible, failure governed by material strength) or long/slender (where additional moments due to lateral deflection under axial load — the P-Δ effect — must be accounted for, reducing load capacity compared to an equivalent short column).

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Columns may be axially loaded (load applied concentrically, producing uniform compressive stress, an idealization since some minimum eccentricity is always assumed in design) or subjected to uniaxial or biaxial bending in combination with axial load (e.g. edge/corner columns, columns with unbalanced beam moments), designed using interaction diagrams relating axial load capacity to moment capacity.

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Longitudinal reinforcement resists axial load and bending; lateral ties (or spirals, for circular/some rectangular columns) hold longitudinal bars in position, provide resistance against buckling of individual bars, and confine the concrete core, improving ductility.

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Footings Footing Type Use Case Isolated footing Supports a single column, proportioned so the net upward soil pressure does not exceed the safe bearing capacity of the soil; designed for bending, one-way (beam) shear, and two-way (punching) shear Combined footing Supports two or more columns on a single footing, used when isolated footings would overlap, be too close to a property line, or where differential settlement between adjacent columns needs to be controlled Pre-stressed Concrete Pre-stressing introduces an internal compressive stress into concrete before service loads are applied, counteracting the tensile stresses that would otherwise develop under load, allowing thinner/longer-span members with reduced or eliminated cracking compared to ordinary reinforced concrete.

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Pre-tensioning: tendons are stressed and anchored before the concrete is cast around them; once the concrete gains sufficient strength, the tendons are released, transferring the prestress to the concrete via bond.

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Post-tensioning: concrete is cast first (with ducts for tendons), and tendons are stressed and anchored against the hardened concrete after it gains sufficient strength.

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Losses in prestress occur due to several causes: elastic shortening of concrete, friction (in post- tensioning, along the duct), anchorage slip, and long-term effects — creep and shrinkage of concrete and relaxation of the steel tendon — all of which reduce the effective prestressing force below the initially applied jacking force.

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This section covers standard and built-up steel sections, bolted and welded connections, and the design of simple steel elements — ties, struts, axially loaded columns, and column bases.

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Standard and Built-up Sections Standard (rolled) sections include I-sections (rolled steel beams/columns), channels, angles, and tees, manufactured to standard dimensions and readily available.

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Built-up sections are fabricated by combining two or more standard sections or plates (e.g. plate girders, laced/battened columns) to achieve section properties (higher moment of inertia, greater capacity) not available in a single standard rolled section, often needed for longer spans or heavier loads.

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Connections Connection Type Characteristics Bolted – bearing type Load transferred through bearing between the bolt shank and the hole surface, and shear in the bolt; relatively simple to design and install, allows some slip before bearing engages Bolted – friction type (HSFG) High-strength friction grip bolts are pre-tensioned to clamp the connected plates together, transferring load through friction between the faying (contact) surfaces; provides a slip-resistant, more rigid connection, often preferred for connections subject to fatigue/reversal of load Welded connections Fillet welds (deposited in the corner between two surfaces, commonly used for lap/tee joints) and butt welds (full-penetration welds joining plate edges, used where a continuous, often stronger, connection is needed); welding offers a more rigid, continuous connection but requires skilled workmanship and quality control Design of Simple Elements Ties (tension members): designed for the applied tensile force considering the net effective cross-sectional area (accounting for bolt holes, if any) against the section's design tensile strength (governed by yielding of gross section or rupture of net section, whichever is critical).

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Struts (compression members) and axially loaded columns: designed against buckling, similar in principle to Euler's column theory but incorporating a design compressive stress that accounts for imperfections and residual stresses (per code buckling curves), based on the member's slenderness ratio.

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Column bases (e.g. slab base): distribute the column's load onto the supporting concrete foundation/footing over a sufficiently large bearing area so the bearing pressure on the concrete does not exceed its permissible bearing stress; anchor bolts secure the base plate to the foundation and resist any uplift/moment.

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This section covers the design principles of timber beams and columns, the design of masonry structures per the Nepal Building Code (NBC), common failure modes of masonry, and the properties of mud, lime, and cement mortars.

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Timber Beams and Columns Timber design uses permissible (working) stresses specific to the timber species and grade, derived from characteristic strength values reduced for factors such as load duration, moisture content, and safety; timber is graded (e.g. by visual grading or stress grading) to sort out defects (knots, grain deviation) that reduce strength.

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Timber beams are designed for bending stress, shear stress (notably horizontal shear along the grain, often more critical than in other materials due to timber's relatively low shear strength parallel to grain), and deflection.

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Timber columns are designed against buckling (similar in principle to Euler's theory, modified for timber's material behaviour) based on the column's slenderness ratio, with permissible compressive stress reducing as slenderness increases.

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Masonry Structures (NBC Provisions) The Nepal Building Code (NBC) provides mandatory rules of thumb — simplified, prescriptive design/detailing rules (e.g. maximum building height/storeys, minimum wall thickness, opening size/placement limits, requirement for horizontal bands at plinth/lintel/roof level, vertical reinforcement at corners/junctions) — for load-bearing masonry buildings, particularly relevant in Nepal's seismic context, allowing safer construction without a full engineering analysis.

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Key masonry properties relevant to design include compressive strength of masonry units and mortar, the resulting masonry assemblage strength, and bond strength between units and mortar.

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Failure Modes of Masonry Failure Mode Description Crushing Compressive failure of masonry units/mortar under excessive vertical (gravity) load Sliding shear Sliding failure along a mortar bed joint when in-plane shear (e.g. from seismic/lateral load) exceeds the joint's shear (friction + bond) resistance Out-of-plane bending/overturning Failure of a wall bending or overturning out of its own plane, particularly critical for unreinforced masonry walls under seismic or wind loading perpendicular to the wall Diagonal tension cracking Diagonal (X-shaped) cracking through masonry units and/or mortar joints, typical of in- plane shear failure of masonry walls/piers under lateral (seismic) loading Mortars Mud mortar: made from clay/soil and water, low cost and traditional, but low strength, low durability (susceptible to erosion/moisture damage), and generally the weakest of the common mortar types.

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Lime mortar: made using lime as the binder, offers better durability and some self-healing (autogenous) capacity for small cracks compared to mud mortar, moderate strength, commonly used in heritage/traditional construction and some load-bearing masonry.

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Cement mortar: made using cement (often with sand, sometimes lime added for workability), offers the highest strength and durability among the three, faster strength gain, and is the standard choice for modern load-bearing and reinforced masonry construction.