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2.0 ANALYSIS AND DESIGN 2.2 STRUCTURAL ELEMENT BEAM Develop by :- NOR AZAH BINTI AIZIZ KOLEJ MATRIKULASI TEKNIKAL KEDAH

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BEAM A beam is a structural member subject to bending.(Flexural member) Its function carrying gravity load in the direction normal to its axis, which results in bending moment and shear force. Bending occurs in member when a component of load is applied perpendicular to member axis, and some distance from a support. Most beams span between two or more fixed points (support).

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Three types of beams:- i)A Simply Supported Beams - both ends are supported by one pin and one roller ii)Cantilever Beams - one end is unsupported, but the other must rigidly built-in top prevent rotation. iii)A continuous Beams - beams with extra supports

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Examples of beams:- i)Beam Slab Bridge Bridge Over Sg. Muda, Kuala Muda Guthrie Corridor Expressway Eleanor

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Types of beam Primary Beam - Beam that supporting by column at the end Secondary Beam - Beam that supporting by another beam at the end

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Types of beam 1.Identify primary beam and secondary beam. A 1 2 C B 1a 4m 2m

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BEAM DISTRIBUTION OF LOADS FROM SLAB TO BEAMS Loads from a slab are transferred to its surrounding beams in either one-way @ two-way depend on the ratio L y /L x L y = longer side, L x = shorter side L y /L x > 2 = one-way slab L y / x ≤ 2 = two-way slab Loads supported by precast concrete slab systems are distributed to beams in one direction only.

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One-way slab Two-way slab Two types of load distribution to beams L y L x L y L x

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Let’s do it now!!!! A 1 2 C B 1a 5.5 m 2.0 m 2.5 m Concrete density: 24 kN/m 3 Dead load characteristic: 1.0 kN/m² (excluding the slab self-weight) Live load characteristic: 2.5 kN/m² Floor thickness: 150 mm 1)sketch the floor tributary areas all for beams. 2)calculate the ultimate design load supported by beam A/1-2 in kN/m considering all floor loadings. Ignoring selfweight of beam. 3) Calculate the maximum shear force and maximum bending moment.

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ANSWER A 1 2 C B 1a 5.5 m 2.0 m 2.5 m Identify one way slab @ two way slab Panel A-B/1-2 LY/LX = 5 / 2 = 2.5 >2 :- one way slab Panel B-C/1-1a LY/LX = 5.5 / 2.5 = 2.2 >2 :- one way slab

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ANSWER Concrete density: 24 kN/m 3 Dead load characteristic: 1.0 kN/m² (excluding the slab self-weight) Live load characteristic: 2.5 kN/m² Floor thickness: 150 mm Self weight slab = 24 x 0.15 = 3.6 kN/m² Total characteristic dead load = 3.6 + 1 = 4.6 kN/m² Design load on slab, w = 1.4 g k + 1.6 q k = 1.4 ( 4.6 ) + 1.6 ( 2.5 ) = 10.44 kN/m²

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ANSWER Design load on beam A/1-2 ( kN/m) = 0.5 x w x l x = 0.5 x 10.44 x 2 = 10.44 kN/m Design load on beam A/1-2 ( kN) = 10.44 kN/m x 5m = 52.2 kN

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ANSWER Maximum shear force V = wL/2 = 10.44 x 5 /2 = 26.1 kN Maximum bending moment M = wL 2 / 8 = 10.44 (5) 2 / 8 = 32.63 kN/m

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Cross Section Detail b h d b - width d – depth h – high F

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F cc = 0.405f cu A cc 0.9 x z= (d-0.9x/2) 0.87fy 0.45fcu b F st = 0.87 f y A s AsAs x d a Where: f cu - Characteristic of concrete strength (30N/mm2) f y - Characteristic of reinforcement strength (460N/mm2) A – area of beam cross section A S – area of reinforcement cross section M – Ultimate Moment Equation ∑M a = 0 F cc (d-0.9x/2) – M = 0 F cc = F st F cc = 0.405f cu A cc @ F cc = 0.45f cu A cc = 0.405 x f cu x b x = 0.45 x f cu x 0.9 x b F st = 0.87 f y A s section stress force M

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Concrete compression A cc = (0.9 x) ( 125) F cc = 0.45f cu x A CC = 0.45f cu x (0.9 x )(125) F st = 0.87 A s F cc A cc 125mm 0.9 x F cc F st Steel tension 0.9x d 0.45f cu 0.87f y

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Example: The beam 6m long shown in Figure with ultimate load of 2kN/m has characteristic material strengths of f cu = 30N/mm 2 for the concrete and f y = 460 N/mm 2 for the steel. Calculate steel area (A s ) and size of rebar to be provided for the beam. 2kN/m 6m

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6 mm Factored load,G k = 2kN/m h = 300mm b = 125mm BEAM DESIGN

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STEP 1 : Calculation of Moment Moment at centre (max) =WL 2 / 8 = 2 x 6 2 /8 = 9kNm 6 mm gk = 2kN/m 9kNm

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h = 300mm b = 125mm STEP 2 : Calculation of d d = h - cover – Φ link – Φ rebar = 300 – 25 – 10 – 12/2 = 259 mm d = mm

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STEP 3 : Force Diagram F st F cc d = 259mm b = 125mm AsAs ∑M a = 0 F cc x ( d - 0.9x / 2) – M = 0 0.45f cu x A cc x (d - 0.9x / 2) – M = 0 z=(d-0.9x/2) a F cc F st

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STEP 3 : Force Diagram 0.405 x 30 x 125 x x ( 259 – 0.9x / 2 ) – 9x10 6 = 0 1518.8x x (259 - 0.45x) – 9 x 10 6 = 0 393369.2x - 683.46x 2 - 9 x10 6 = 0 683.46x 2 – 393369.2x + 9x10 6 = 0 x = -b + b 2 -4ac x = 551.7mm @ 23.9mm F cc = 0.405 x 30 x 23.9 x 125 = 36298N = 36.3kN 2a

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F cc = F st 36298N = 0.87f y x A s A s = 36298 / 0.87(460) = 90.70 mm 2 So size rebar A = Ωj 2 = Ω D 2 / 4 = 90.70mm 2 A = 90.70 /2 = 45.35mm D = 45.35 x 4 / Ω D = 7.6 mm for 2 bar So size rebar for the beam is 8mm. h = 300mm b = 125mm A s = 90.70 mm2 D = 8mm :. size rebar to be provided is 2 T 8

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COLUMN

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Vertical elements which are normally loaded in compression.(compression member) 2 types :- i) Strut – small member in a framed structure ii) Column – larger member as a main support for a beam in a building Axial loaded compression members can fail in two principal ways: i) short fat member fail by crushing or splitting of the material. ( strength criterion) ii) long thin members fail by sideways buckling. (stiffness criterion)

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DESIGN COLUMN Ultimate compressive load capacity, N = sum of the strengths of both the concrete and steel components. N= 0.4 f cu A c + 0.75 f y A sc f cu = characteristic concrete cube crushing strength f cu = area of concrete f y = characteristic yield stress of steel A sc = area of steel Table 1 Diameters and areas of reinforcing bars Bar dia.(mm)6 8 10 12 16 20 25 32 40 C/s area (mm 2 )28 50 79 113 201 314 491 804 1256

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Design Column A short reinforced concrete column is to support the following axial loads : characteristic dead load : 758 kN characteristic live load : 630 kN If the column is to measure 325 mm x 325 mm and the concrete characteristic strength is 30 N/mm2, determine the required size of high yield reinforcing bars. Design load = 1.4 Gk + 1.6 Qk = 1.4 (758) + 1.6 (630) = 2069 KN N= 0.4 fcu Ac + 0.75fy Asc 2069 x 10 3 = 0.4 ( 30 ) 325 2 + 0.75 ( 460) Asc 801500 = 0.75 x 460 x Asc Asc = 2323 mm 2 Consider 4 bars are used: Asc = 2323 mm 2 4 = 581 mm2 From Table 1 ; area 32 mm dia. Bar = 804 mm 2 Size of rebar required = 4T32

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The foundation of a building is that part of walls, piers and columns in direct contact with, and transmitting loads to, the ground. The building foundation is sometimes referred to as the artificial foundation, and the ground on which it bears as the natural foundation. FOUNDATION DESIGN

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The primary functional requirement of a foundation is strength and stability. Strength and stability The combined, dead, imposed and wind loads on a building must be transmitted to the ground safely, without causing deflection or deformation of the building or movement of the ground that would impair the stability of the building and/or neighboring structures. Foundations should also be designed and constructed to resist any movements of the subsoil. FOUNDATION DESIGN

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