Definitions and Details

Reinforced Concrete Design to EC2 - Definitions and Details– Basics

Overall Depth of Beam – h (mm)

Breadth of Beam – b (mm)

Effective Depth of Beam – d (mm) - From top of beam to Centroid of Steel

Effective Span of Beam – L (m)- SSB – Lesser of centre of bearing to centre of bearing or

clear span + effective depth.- Cantilever - clear length + ½ effective depth.- Continuous - centre of bearing to centre of bearing.

Singly Reinforced Concrete Section

Cover to Reinforcement (mm) – For Durability: depends on concrete strength class and environmental conditions – (EC2 Tables 4.1 & NA2)– For Fire Resistance: less likely to be critical – (Tables 5.2a of EC2 Part 1-2)– For Casting Conditions see 4.4.1.3 (4)

Characteristic compressive cylinder strength of concrete, fck (N/mm2)

Concrete Compressive Strength ClassA classification comprising the type of concrete (normal-weight or lightweight), the minimum characteristic 150 mm diameter by 300 mm cylinder strength and the minimum characteristic 150 mm cube strength eg C20/25 (ie fck = 20 N/mm2)

Concrete Density (unit weight) = 25 kN/m3

Characteristic tensile strength of reinforcement, fyk (N/mm2)- High yield steel (hot rolled or cold worked) fyk = 500 N/mm2 - H Bars

(except where higher ductility steel is specified then the notation used is B or C Bars)

Reinforcement Details – Min No of rebars = 2, Max No of rebars = 8 – Main bar diameter, = 16 - 40mm

– Min clear spacing = max aggregate size + 5mm (= 25mm), or Max bar or 20mm

Max Area of Steel Reinforcement = 0.04bh (mm2)

Min Area of Steel Reinforcement should not be less than 0.00016 fck2/3bd or 0.0013bd (mm2)

Max &spacing of bars –see Table 5.6 –ISE Manual for the design of concrete building structures to EC 2

(add 1 bar to clear spacing to give bar spacing)

Design Ultimate Load, F = 1.35×Dead Load+ 1.5× Imposed Load (kN) (the Factored Load) EC 0

(F = 1.35×Gk+ 1.5×Qk)

Design Ultimate Moment, MEd = FL/8, FL/4, FL/6, (kNm) (Design value of the applied internal bending moment)

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Definitions and Details

Singly Reinforced Beam – shown above. Steel resists Tension, Concrete resists Compression

Hanger Bars – typically 2 H12 or 2H16, Links HANG from them. Links – Min = 8 mm Doubly Reinforced Beam –Additional steel designed in the compression zone to increase the compression resistance of the section

Effective Depth of Beam, d = h – cover – link½ main bar

Deflection – is controlled by ensuring that the span depth ratio does not exceed allowable limits.

Cracking may be controlled by limiting the & spacing of rebars (0.3mm is usual)

Lever Arm, z – the distance between the centres of the compression and tension zones of the stress block.

Lever Arm Factor, z/d – the ratio of lever arm to effective depth, must be between 0.82 ≤ z/d ≤ 0.95

Main Beam, Secondary Beam and Column Reinforcement

RC Design to EC2- Definitions and Details - SHEAR

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Definitions and Details

Simply Supported Unreinforced Concrete Beam

Where BM is greatest: Cracks are caused by Bending Stress in the tension zoneWhere SF is greatest: Cracks are caused by Diagonal Tension / Diagonal Compression due to complementary shears

EC2 uses the strut inclination method for shear design.Shear Resistance is provided by inclined concrete struts acting in compression and

shear reinforcement acting in tension.

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Link spacing = s

Shear symbols have a w subscript.

Minimum width of beam web = bw (is equal to b for rectangular sections) (show symbols on diagram on left)

The beam behaves like a truss z mm deep

Definitions and Details

Shear design must show that the applied shear stress on the beam is less than its shear resistance (shear capacity), which is the method used by Concise Eurocode 2 (Concrete Centre publication).

The Design Shear Stress vEd, @ ULS is given by: vEd = VEd/bw0.9d (= VEd/bwz)

VEd is the Design value of the applied shear force on the section,

bw is the Breadth,

d is the Effective Depth of the beam, (z is assumed to be 0.9d)

Capacity of Concrete StrutsvEd is then checked against vRd,max , the Capacity (Resistance) of Concrete Struts expressed as a stress

from Table 7.2 (CEC2),

For beams with low shear stress:

vEd ≤ the value of vRd,max for = 21.8o, the minimum strut angle and cot= 2.5

For beams with high shear stress:

vRd,max for = 21.8o ≤vEd ≤ vRd,max for = 45o, the maximum strut angle and 2.5 ≥ cot≥ 1

If the value of vRd,max for = 45o < vEd, then the capacity of the concrete is exceeded and the section size or the concrete design strength must be increased.

Shear Reinforcement The characteristic yield strength of the shear reinforcement fywk = 500 N/mm2 - H Bars

The ratio of cross sectional area of shear reinforcement to link spacing, Asw/s ≥ vEd bw / fywd cotwhere Asw = Area of Shear Steel, in mm2, & Link Spacing = s, where max s = 0.75d mm,

fywd = fywk /s = design yield strength of the shear reinforcement = 500/1.15 = 435 N/mm2

Asw/s ratios are found from standard rebar tables

If the strut angle is 21.8o, then cot = 2.5,

and Asw/s is given by: Asw/s ≥ vEd bw/1087 mm2/mm

If the angle is between 21.8o & 45o, then cot is calculated from = 0.5 sin-1[vEd /0.20 fck(1 - fck/250)]

and Asw/s is given by: Asw/s ≥ vEd bw/435cot mm2/mm

Shear Reinforcement ChecksThe minimum Asw/s ratio is given by Asw/s ≥ 0.08 × fck

0.5× bw / 500 mm2/mm

The minimum link spacing is 75mm and the maximum link spacing is 0.75d

2 19H12 – 06 – 300 5H12 – 06 – 200

RC Design to EC2- Definitions and Details - DEFLECTION

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Definitions and Details

Beam Deflection (& concrete cracking) checks must be carried out at the Serviceability Limit State, to control deflection & concrete cracking under service (ie working) loading. The empirical approach adopted limits the deflection to span/250 (compare with steel & timber).

The actual span to depth ratio L/d is calculated and is then compared to the allowable span to depth ratio.

A basic span to depth ratio is determined and is modified by a series of factors to give

Allowable L/d = N x K x F1 x F2 x F3 ≥ Actual L/d

N = the basic span-to-effective-depth ratio dependent on % reinforcement and concrete strength.

K = a factor to account for the structural system

F1 = a factor to account for flanged sections.

F2 = 1.0 generally (A factor to account for brittle partitions in association with long spans)

F3 = a factor to account for the service stress in tensile reinforcement = 310/s but upper limit of F3 = 1.5

Where service stress, s = 435 × (Gk + 0.3×Qk /1.35×Gk + 1.5×Qk) × (As req / As prov) N/mm2

As req is the area of tension reinforcement required at the section considered for the ultimate limit state.

As prov is the area of reinforcement actually provided.

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