48353-CD-S24-Lecture-10 Slides.pdf

48353 Concrete Design Spring 2024 Lecture 10: Introduction to RC Columns A/Professor Shami Nejadi CB11.11.111, [email protected] School of Civil and Environmental Engineering UTS CRICOS...

48353 Concrete Design Spring 2024 Lecture 10: Introduction to RC Columns A/Professor Shami Nejadi CB11.11.111, [email protected] School of Civil and Environmental Engineering UTS CRICOS 00099F LECTURE 10 - OUTLINE Introduction to RC Columns Types of Columns Failure Mode Reinforcement requirements for columns RC columns in pure compression ΦNuo Plastic centroid Example School of Civil and Environmental Engineering Introduction to RC Columns What is a column ? – a member in any orientation that primarily carries compression and whose cross-sectional dimensions are small compared to its length. – In this subject columns will be vertical elements. What does it do? – A column directly transfers vertical loads in a structure by compression through the footings/foundations to the ground. – A column may also transfer horizontal loads on a structure by bending. 3 Introduction to RC Columns N Apart from horizontal loading, N M m om ents also develop in columns if there are unbalanced vertical loads (e.g. in exterior columns), imperfections, initial out-of-straightness, and eccentricity of applied loads from slabs/beams. Columns are always designed as beam-columns according to AS M 3600 for strength (emin = 0.05 D ), N N where D is the overall depth. Column Beam-column 4 Introduction to RC Columns Figure 10.1 shows that the force P applied at an eccentricity “e” is equivalent to an axial force P and a moment M, where M=P.e The moment will generate a variation from flexural tension to flexural compression across the cross-section, we refer to the tension and compression sides of a column section. Figure 10.1 Introduction to RC Columns Columns can take a variety of forms, most commonly: – Square – Rectangular – Circular Non-standard or irregular shaped cross-sections can also be used. Composite columns come in a variety of configurations e.g. structural steel section encased in concrete (Fig 12.2.e), or steel hollow sections (CHS, SHS, or RHS) filled with concrete (Fig 10.2.f). 6  Min. 4 bars Introduction to RC Columns Min. 6 bars Bars in corners Figure 10.2 7 Reinforcement Requirements for Columns RC columns contain longitudinal reinforcing to resist the axial compression and moment (main reinforcement, on all sides). For square and rectangular columns, the minimum number of longitudinal reinforcing bars is 4, one in each corner. For circular columns the minimum number of longitudinal reinforcing bars is 6, equally spaced. For irregular shapes, some judgment required for the number of bars, but longitudinal bars must be adjacent to all exterior and re-entrant corners (see Fig. 10.2.c). 8 Reinforcement Requirements for Columns A long bar will easily undergo Euler buckling. The strength of the concrete cover between the bar and the surface is not enough to stop the bar from buckling and bursting out of the column (see Figure 10.3). Transverse reinforcement is provided either as closely spaced fitments or a helix, to prevent outward buckling of the longitudinal bars and spalling of the core concrete (secondary reinforcement). This reinforcement also provides confinement to the core concrete which increases the strength and the ductility of the column. Figure 10.3 9 Reinforcement Requirements for Columns 10 Reinforcement Requirements for Columns 11 Reinforcement Requirements for Columns In most cases the total amount of main longitudinal reinforcement (As = Asc +Ast) is restricted to a range of: - (a) min 1% (to provide a minimum flexural strength) & - (b) max 4% (to prevent congestion of bars and difficulty in pouring & compacting the concrete) of A g , Cl. 10.7.1. Cl. 10.7.1(a): The total area of longitudinal steel provided must be at least As = 0.01 Ag - where: Ag = b × D D is the overall depth of the cross-section b is the width of the cross-section 12 Reinforcement Requirements for Columns Cl. 10.7.4.3 (a): Minimum size of ties to be used, depends on the maximum size of the longitudinal bars (see Table 10.7.4.3). 13 Reinforcement for for Requirements Reinforcement Requirements Columns Columns Cl. 10.7.4.3 (b): - Maximum spacing of the ties, shall not exceed the smaller of: - Dc and 15db for single bars. - Or 0.5Dc and 7.5db for bundled bars. where: Dc = smaller column cross-sectional dimension or diameter. db = diameter of the smallest bar in the column. 14 Reinforcement Requirements for Columns 15 Reinforcement Requirements for Columns 16 Reinforcement Requirements for Columns 17 RC Columns in Pure Compression ΦNuo Reinforced concrete columns are never designed for pure compression only. Thus this case needs to be checked whether a column is short or slender. Cl. 10.1.3.2 Short columns : columns in which the additional bending moments due to slenderness can be taken as zero. (If P ∆ effect is negligible column is short) Cl. 10.1.3.3 Slender column : columns that does not satisfy the requirements for a short column. Cl.10.1.3.1 Braced columns : columns in a structure for which the lateral actions applied at the ends are resisted by shear walls, lateral bracing or masonry infill panels (See Fig 10.4-a). 18 Figure 10.4 19 Limit State Design for Columns 20 RC Columns in Pure Compression ΦNuo Cl.10.6.2; Strength of cross-section using ERSB - Squash load (Nuo) : Nominal ultimate strength in pure compression, calculated by assuming that there is a uniform concrete compression stress of α1f’c and that the steel and concrete have a maximum strain of 0.0025. ε cu = ε sy = 0.0025 0.0025 0.0022 0.0025 21 RC Columns in Pure Compression ΦNuo Limiting strain criterion in ax ial com pression as: εc = 0.0025 0.0025 = =α1f ’c σc = α1 f’c σs Nu = σc.Ac + σs.As 22 RC Columns in Pure Compression ΦNuo Peak axial load (ultimate) can be determined as : N uo = α 1 f’ c.A c + f sy.A s where A c = A g – A st , Ag = section gross area & As= total steel area AS3600 Cl. 10.6.2.2; the coefficient α1 is: α1 = 1.0 – 0.003 f’c where 0.72 ≤ α1 ≤ 0.85 N uo is often referred to as the Squash Load. For design capacity, ΦNuo we refer to Table 2.2.2, which shows Φ = 0.65 for compression. 23 (AS 3600-2018) 24 Plastic Centroid For all combinations of applied compression and moment, the applied axial load at failure is assumed to act through a point on the cross-section called the plastic centroid. Assuming the applied axial load at failure acts through this point ensures a uniform compressive strain across the cross-section. If the applied moment is represented by the compression force acting at an eccentricity e, this eccentricity is measured from the plastic centroid. 25 Plastic Centroid For symmetric sections that are symmetrically reinforced, the plastic centroid is at the geometric centroid. For asymmetric sections (either in concrete geometry or in reinforcement arrangement) the position of the plastic centroid must be calculated. The position of the plastic centroid may be calculated by equating moments of the forces on the cross-section: Nuo x (dpc) = Fc × (D/2) + Σ Fsi × dsi 26 Plastic Centroid Ac × α1 f c' × D / 2 + A1 × f sy × d1 + A2 × f sy × d 2 d PC = NUO where Nuo = α1 f’c.Ac + fsy.As Example-10.1 10.5 AN32= 800 mm2 Figure 10.5 28 Example-10.1 α1 = 1.0 – 0.003f’c Squash Load: where Nuo = α1 f’c.Ac + fsy.As Ac = 600 × 800 − (π ×150 2 / 4) − 8 × 800 = 456 ×103 mm 2 N uo = 0.85 × 40 × 456 × 103 + 500 × 8 × 800 = 18704kN 29 Example-10.1 α1 f c' Ac × D / 2 + A1 × f sy × d1 + A2 × f sy × d 2 + A3 × f sy × d 3 d PC = NUO N uo d PC = 0.85 × 40 × 456 ×103 × 800 / 2 + 3 × 800 × 500 × 66 + 2 × 800 × 500 × 400 + 3 × 800 × 500 × 734 = 7.48 × 109 The depth to the plastic centroid is thus calculated as: 7.48 ×109 d PC = = 400mm 18704