beam design

RC Beam Design Procedure

Reinforced Concrete Beam Design Procedure –

Main

Reinforcement

DATA State

DURABILITY & State Determine Calculate

Effective Span of Beam – L (m) Concrete Compressive Strength Class C?/? Characteristic compressive cylinder strength of concrete, fck (N/mm2) Characteristic strength of Reinforcement, fyk (500 N/mm2) Breadth of Beam – b (mm) Overall Depth of Beam – h (mm) Characteristic Loadings – Dead and Imposed (kN, kN/m, kN/m2) Main Bar φ – 16 - 40mm Link Bar φ – 8 - 12mm

FIRE RESISTANCE Exposure Class from T 4.1 (EC2) & Required Fire Resistance (mins) Nominal Cover (mm) from T NA.2 (NA to EC 2) & T 5.2a (EC 2 Part 1-2) Effective Depth of Beam, d = h – cover – linkφ − ½ main barφ (mm)

LOADING @ ULS Calculate Design Ultimate Load, F = 1.35DL + 1.5 IL (kN) (=1.35×Gk + 1.5×Qk

EC 0)

MOMENT @ ULS Calculate Design Ultimate Moment, MEd (=FL/8, =FL/4, =FL/6, etc) (kNm) Calculate

K = MEd/bd2fck

Show that

K < 0.167 (K’)

Calculate

Lever Arm Factor z/d = 0.5 + √( 0.25 – 0.882K )

Show that

0.82 ≤ z/d ≤ 0.95

Calculate

Lever Arm, z = z/d × d (mm)

(use N & mm)

State No compression steel required

State z/d OK

MAIN REINFORCEMENT Calculate Required Area of steel reinforcement, As = MEd / 0.87fykz (mm2) Determine Show that

(use N & mm)

Number & φ

of bars, such that Provided As > Required As (e.g. Use 3H25 (1470mm2) ) As is between Max & Min Limits: 0.0013bd ≤ 0.00016 fck2/3bd ≤ As ≤ 0.04bh (mm2) State As OK

CRACKING @ SLS Sketch A section through the beam showing the main bars, links, clear & bar spacing. Show that

Clear spacing is greater than minimum limits = 25mm, or max bar φ .

Calculate

Service stress, σs & hence the max bar φ

Show that

Bar diameter OR bar spacing is less than the maximum values from T5.6 State Cracking OK 1

& spacing from T 5.6 (ISE Manual)

RC Beam Design Procedure

Reinforced Concrete Beam Design Procedure –

Shear

Reinforcement

SHEAR @ ULS Determine

Design value of the applied Shear Force, VEd (kN) = Max SF from SFD, at the support for a SSB

Calculate

Design Shear Stress, vEd

= VEd/bw0.9 d (N/mm2)

State bW

CONCRETE STRUT CHECK Determine Capacity of Concrete Struts, vRd,max (N/mm2) from Table 7.2 (Concise EC2), for θ o and fck For beams with low shear stress: Show that vEd < vRd,max

State that

θ = 21.8o, look up vRd,max value in bold column:

∴ cotθ = 2.5

State OK against crushing Go to Shear Reinforcement

For beams with high shear stress: 21.8o < θ column: Show that vEd < vRd,max

< 45, look up vRd,max value in other

Calculate

θ = 0.5 sin-1[vEd /0.20 fck(1 - fck/250)]

Show that

cotθ

crushing

Calculate cotθ

>1.0

State OK against Go to Shear Reinforcement

SHEAR REINFORCEMENT For beams with low shear stress Calculate vEd bw/1087 (mm2/mm)

Assume

Asw/s (mm2/mm) Asw = Area of Shear Steel, in mm2, & Link Spacing = s, where max s = 0.75d mm,

Show that

Asw/s ≥ vEd bw /1087 (mm2/mm)

Refer to Rebar Ratio Tables

Go to Shear Reinforcement Checks

For beams with high shear stress

Calculate

vEd bw/435cotθ

Assume

Asw/s (mm2/mm) Asw = Area of Shear Steel, in mm2, & Link Spacing = s, where max s = 0.75d mm,

Show that

Asw/s ≥ vEd bw /435cotθ

SHEAR REINFORCEMENT CHECKS Calculate 0.08 fck0.5 bw /500 (mm2/mm)

Show that

(mm2/mm)

Refer to Rebar Ratio Tables

Go to Shear Reinforcement Checks

Minimum value

Asw/s ≥ 0.08 fck0.5bw /500 (mm2/mm)

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State Asw/s OK

RC Beam Design Procedure

Show that

75 < s < 0.75d (mm)

State

Bar Type, φ ,

200)

State Link Spacing OK

and Spacing of Links

eg H8 @ 200c/c

Reinforced Concrete Beam Design Procedure–

(H8-03-

Deflection

Check

DEFLECTION @ SLS Calculate Actual span-to-effective-depth ratio, L/d Calculate

Required tension reinforcement ratio, ρ = (As,req /bd)×100

Determine Determine

Basic span-to-effective-depth ratio, N from Table 15.10. (Concise EC2), for ρ and fck Factor K from Table 15.11. (Concise EC2), for beam type

Calculate

beff/bw

Determine

Factor F1 from Table 15.12. (Concise EC2), for flanged beam geometry.

State that

Factor F2 = 1 for non brittle partitions over a 7m+ span

(%

)

beff = bw for rectangular sections

Service stress, σs = 435×(Gk + 0.3Qk /1.35×Gk + 1.5×Qk)×(As req /As prov)

State (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.

Calculate

Factor F3 to account for service stress in tensile reinforcement = 310/σs ≤ 1.5

Calculate

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

Show that

Actual L/d ≤ Allowable L/d

State Deflection OK

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RC Beam Design Procedure

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