_____________________________________________________________________
Company Name : HP LEE CONSULT
Designed by :
Date and Time : Wednesday, July 01, 2015 11:54:55 AM
(License Number: Timer-SN243-C0-1)
_____________________________________________________________________
MATERIAL AND DESIGN DATA
Code of Practice fcu (N/mm²) Ec, (N/mm²) fy (N/mm²) fyv (N/mm²) γc γs
BS8110 : 1997 30 24597 460 460 1.5 1.05
Cover (mm) Side Cover (mm) Conc. Unit Weight (kN/m³) Steel Unit Weight (kg/m³)
25 25 24 7860
Beam Design Detail Report
DETAIL CALCULATION FOR BEAM GB4(150x450)
Beam Located along grid B1A/1A1-2A1
Number of Span within beam = 2
Number of Section defined by user = 2
Number of Supports = 3
Beam Cantilever End = Nil.
Section Dimension Data
Length Width Begin Depth End Depth
Span Section
(mm) (mm) (mm) (mm)
1 1 3300 150 450 450
2 2 3300 150 450 450
MATERIAL PROPERTIES
Maximum Concrete Strain, Ecc = 0.0035
Average Concrete Stress above Neutral Axis, k1 = 12.12 N/mm²
Concrete Lever Arm Factor, k2 = 0.4518
Limiting Effective Depth Factor, cb = 0.50
k2 / k1 Factor, kkk = 0.0373
Limiting Concrete Moment Capacity Factor, kk1 = cb × k1 × (1 - cb * k2) = 0.50 × 12.12 × (1 - 0.50 × 0.4518) = 4.6911 N/mm²
BEAM GB4(150x450) SPAN NO. 1
FLEXURAL DESIGN CALCULATION
LOCATION : SPAN
Design Bending Moment = 1.8 kNm Width, b = 150.0 mm Effective Depth, d = 409.0 mm
Mu / bd² = 1.8 × 1000000 / (150.0 × 409.0²) = 0.072 N/mm²
Singly Reinforced Design, limit Mu / bd² < kk1
Mu / bd² = 0.072 <= 4.691
Design as Singly Reinforced Rectangular Beam
Concrete Neutral Axis, x = 2.428 mm
Concrete Compression Force, Fc = k1 × b × x / 1000 = 12.12 × 150 × 2.428 / 1000 = 4.41 kN
Steel Area Required, AsReq = Fc × 1000 / (fy / γs) = 4.41 × 1000 / (460 / 1.05) = 11 mm²
Moment Capacity = Fc × (d - k2 × x) / 1000 = 4.41 × (409.0 - 0.4518 × 2.428) / 1000 = 1.8 kNm
Maximum Depth of Section = 450.0 mm
Minimum Tension Steel Area Required = 0.13% × 150.0 × 450.0 = 88 mm²
Top Compression Steel Area Required = 88 mm²
Bottom Tension Steel Area Required = 88 mm²
License Number: Timer-SN243-C0-1
1/10
Top Reinforcement Provided = 2T12 (226 mm²)
Bottom Reinforcement Provided = 2T12 (226 mm²)
LOCATION : LEFT SUPPORT
Design Bending Moment = 0.0 kNm Width, b = 150.0 mm Effective Depth, d = 409.0 mm
Mu / bd² = 0.0 × 1000000 / (150.0 × 409.0²) = 0.000 N/mm²
Design to minimum steel percentage specified by code,
Maximum Depth of Section = 450.0 mm
Minimum Tension Steel Area Required = 0.13% × 150.0 × 450.0 = 88 mm²
Top Tension Steel Area Required = 88 mm²
Top Reinforcement Provided = 2T12 (226 mm²)
Bottom Reinforcement Provided = 2T12 (226 mm²)
LOCATION : RIGHT SUPPORT
Design Bending Moment = 4.5 kNm Width, b = 150.0 mm Effective Depth, d = 409.0 mm
Mu / bd² = 4.5 × 1000000 / (150.0 × 409.0²) = 0.180 N/mm²
Singly Reinforced Design, limit Mu / bd² < kk1
Mu / bd² = 0.180 <= 4.691
Design as Singly Reinforced Rectangular Beam
Concrete Neutral Axis, x = 6.110 mm
Concrete Compression Force, Fc = k1 × b × x / 1000 = 12.12 × 150 × 6.110 / 1000 = 11.11 kN
Steel Area Required, AsReq = Fc × 1000 / (fy / γs) = 11.11 × 1000 / (460 / 1.05) = 26 mm²
Moment Capacity = Fc × (d - k2 × x) / 1000 = 11.11 × (409.0 - 0.4518 × 6.110) / 1000 = 4.5 kNm
Maximum Depth of Section = 450.0 mm
Minimum Tension Steel Area Required = 0.13% × 150.0 × 450.0 = 88 mm²
Top Tension Steel Area Required = 88 mm²
Bottom Compression Steel Area Required = 88 mm²
Top Reinforcement Provided = 2T12 (226 mm²)
Bottom Reinforcement Provided = 2T12 (226 mm²)
LOCATION : 1/4 SPAN
Design Bending Moment = 1.1 kNm Width, b = 150.0 mm Effective Depth, d = 409.0 mm
Mu / bd² = 1.1 × 1000000 / (150.0 × 409.0²) = 0.044 N/mm²
Singly Reinforced Design, limit Mu / bd² < kk1
Mu / bd² = 0.044 <= 4.691
Design as Singly Reinforced Rectangular Beam
Concrete Neutral Axis, x = 1.484 mm
Concrete Compression Force, Fc = k1 × b × x / 1000 = 12.12 × 150 × 1.484 / 1000 = 2.70 kN
Steel Area Required, AsReq = Fc × 1000 / (fy / γs) = 2.70 × 1000 / (460 / 1.05) = 7 mm²
Moment Capacity = Fc × (d - k2 × x) / 1000 = 2.70 × (409.0 - 0.4518 × 1.484) / 1000 = 1.1 kNm
Maximum Depth of Section = 450.0 mm
Minimum Tension Steel Area Required = 0.13% × 150.0 × 450.0 = 88 mm²
Top Tension Steel Area Required = 88 mm²
Bottom Compression Steel Area Required = 88 mm²
Top Reinforcement Provided = 2T12 (226 mm²)
Bottom Reinforcement Provided = 2T12 (226 mm²)
SHEAR & TORSION DESIGN CALCULATION
LOCATION : SECTION 1 LEFT SUPPORT
License Number: Timer-SN243-C0-1
2/10
(B:0 mm E:825 mm from left grid of span)
Maximum Torsion within Zone, T = 0.0 kNm
Shear at Location of Maximum Torsion, V = 2.9 kN
Link Horizontal Dimension, h1 = b - 2 × Side Cover - DiaLink = 150 - 2 × 25 - 10 = 90 mm
Link Vertical Dimension, v1 = h - 2 × Cover - DiaLink = 450 - 2 × 25 - 10 = 390 mm
Dimension x1 = Min (h1, v1) = 90 mm, y1 = Max (h1, v1) = 390 mm
Section Dimension: Dmin = 150.0 mm, Dmax = 450.0 mm
Torsion Stress, νst = 2 × T × 106 / (Dmin² × (Dmax - Dmin / 3)) = 0.00 N/mm²
Effective depth, d = 409.0 mm
Shear Stress, νss = V × 1000 / (b × d) = 2.9 × 1000 / (150.0 × 409.0) = 0.05 N/mm²
Part 2 : Clause 2.4.6 and Table 2.3
Maximum Combined Stress Allowed, νtu = Min (0.8 × √fcu, 5) = 4.38 N/mm²
Total Stress, νTot = νss + νst = 0.05 + 0.00 = 0.05 N/mm² ≤ νtu (4.38 N/mm²)
Checking for Combined Stress Allowed Pass
Part 2: Clause 2.4.5
Additional Checking While Small Cross Section (y1 < 550 mm)
Larger Link Dimension, y1 = 390.0 mm < 550 mm
νtu × y1 / 550 = 4.38 × 390.0 / 550 = 3.11 N/mm²
νst = 0.00 N/mm² ≤ 3.11 N/mm²
Checking for Torsion Stress Allowed Pass
Part 2 : Clause 2.4.6 Table 2.3
Torsion Strength contributed by concrete, νt,min = Min (0.067 × √fcu, 0.4) = 0.37 N/mm²
Torsion Stress, νst = 0.00 N/mm² < νt,min = 0.37 N/mm² -> No Torsion Reinforcement is needed
Maximum Shear within Zone, V = 2.6 kN
Maximum Shear Stress Allowed, νMax = Min (0.8 × √30, 5) = 4.38 N/mm² - Clause 3.4.5.2
Shear Stress, νss = V × 1000 / (b × d) = 2.6 × 1000 / (150.0 × 409.0) = 0.04 N/mm² ≤ νMax (4.38 N/mm²)
Checking for Maximum Shear Stress Allowed Pass
Tension Steel Area Provided, Ast = 226 mm²
- Table 3.8: Values of νc, design concrete shear stress
Steel Percentage, 100 × As / (bv × d) = 0.37 % ≤ 3.0 %
Effective Depth Ratio, edr = 400 / d = 400 / 409.0 = 0.978
(400 / d)^ ¼ = 0.994 < 1, (400 / d)^ ¼ taken as 1
Minimum fcu, fcuMin = 25 N/mm², Concrete Grade Ratio, Min(fcu, 40) / fcuMin = 30 / 25 = 1.200
Concrete Shear Capacity, νc = 0.79 {100 As / (bv d)}⅓ (400 / d)¼ (fcu / 25)⅓ / γm
= 0.79 × {0.37}⅓ × 1.000 × (1.200)⅓ / 1.25 = 0.48 N/mm²
Minimum Design Shear Stress, νMin = 0.40 N/mm²
νss = 0.043 < νc + 0.4, Provides only minimum link
Design for minimum Shear Stress, νd = νmin = 0.40 N/mm²
Shear Link Area / Spacing Ratio, SAsv_Sv = (vd × b) / (fyy × fy) = (0.40 × 150) / (0.95 × 460) = 0.137 mm²/mm
Shear Reinforcement Provided : T10-250 (Link spacing is governed by user setting)
Shear Link Area / Spacing Ratio Provided = 0.628 mm²/mm > 0.137 mm²/mm
LOCATION : SECTION 1 MIDDLE ZONE
(B:825 mm E:2475 mm from left grid of span)
Maximum Torsion within Zone, T = 0.0 kNm
Shear at Location of Maximum Torsion, V = 0.5 kN
Link Horizontal Dimension, h1 = b - 2 × Side Cover - DiaLink = 150 - 2 × 25 - 10 = 90 mm
Link Vertical Dimension, v1 = h - 2 × Cover - DiaLink = 450 - 2 × 25 - 10 = 390 mm
Dimension x1 = Min (h1, v1) = 90 mm, y1 = Max (h1, v1) = 390 mm
License Number: Timer-SN243-C0-1
3/10
Section Dimension: Dmin = 150.0 mm, Dmax = 450.0 mm
Torsion Stress, νst = 2 × T × 106 / (Dmin² × (Dmax - Dmin / 3)) = 0.00 N/mm²
Effective depth, d = 409.0 mm
Shear Stress, νss = V × 1000 / (b × d) = 0.5 × 1000 / (150.0 × 409.0) = 0.01 N/mm²
Part 2 : Clause 2.4.6 and Table 2.3
Maximum Combined Stress Allowed, νtu = Min (0.8 × √fcu, 5) = 4.38 N/mm²
Total Stress, νTot = νss + νst = 0.01 + 0.00 = 0.01 N/mm² ≤ νtu (4.38 N/mm²)
Checking for Combined Stress Allowed Pass
Part 2: Clause 2.4.5
Additional Checking While Small Cross Section (y1 < 550 mm)
Larger Link Dimension, y1 = 390.0 mm < 550 mm
νtu × y1 / 550 = 4.38 × 390.0 / 550 = 3.11 N/mm²
νst = 0.00 N/mm² ≤ 3.11 N/mm²
Checking for Torsion Stress Allowed Pass
Part 2 : Clause 2.4.6 Table 2.3
Torsion Strength contributed by concrete, νt,min = Min (0.067 × √fcu, 0.4) = 0.37 N/mm²
Torsion Stress, νst = 0.00 N/mm² < νt,min = 0.37 N/mm² -> No Torsion Reinforcement is needed
Maximum Shear within Zone, V = 2.8 kN
Maximum Shear Stress Allowed, νMax = Min (0.8 × √30, 5) = 4.38 N/mm² - Clause 3.4.5.2
Shear Stress, νss = V × 1000 / (b × d) = 2.8 × 1000 / (150.0 × 409.0) = 0.05 N/mm² ≤ νMax (4.38 N/mm²)
Checking for Maximum Shear Stress Allowed Pass
Tension Steel Area Provided, Ast = 226 mm²
- Table 3.8: Values of νc, design concrete shear stress
Steel Percentage, 100 × As / (bv × d) = 0.37 % ≤ 3.0 %
Effective Depth Ratio, edr = 400 / d = 400 / 409.0 = 0.978
(400 / d)^ ¼ = 0.994 < 1, (400 / d)^ ¼ taken as 1
Minimum fcu, fcuMin = 25 N/mm², Concrete Grade Ratio, Min(fcu, 40) / fcuMin = 30 / 25 = 1.200
Concrete Shear Capacity, νc = 0.79 {100 As / (bv d)}⅓ (400 / d)¼ (fcu / 25)⅓ / γm
= 0.79 × {0.37}⅓ × 1.000 × (1.200)⅓ / 1.25 = 0.48 N/mm²
Minimum Design Shear Stress, νMin = 0.40 N/mm²
νss = 0.045 < νc + 0.4, Provides only minimum link
Design for minimum Shear Stress, νd = νmin = 0.40 N/mm²
Shear Link Area / Spacing Ratio, SAsv_Sv = (vd × b) / (fyy × fy) = (0.40 × 150) / (0.95 × 460) = 0.137 mm²/mm
Shear Reinforcement Provided : T10-250 (Link spacing is governed by user setting)
Shear Link Area / Spacing Ratio Provided = 0.628 mm²/mm > 0.137 mm²/mm
LOCATION : SECTION 1 RIGHT SUPPORT
(B:2475 mm E:3300 mm from left grid of span)
Maximum Torsion within Zone, T = 0.0 kNm
Shear at Location of Maximum Torsion, V = 5.3 kN
Link Horizontal Dimension, h1 = b - 2 × Side Cover - DiaLink = 150 - 2 × 25 - 10 = 90 mm
Link Vertical Dimension, v1 = h - 2 × Cover - DiaLink = 450 - 2 × 25 - 10 = 390 mm
Dimension x1 = Min (h1, v1) = 90 mm, y1 = Max (h1, v1) = 390 mm
Section Dimension: Dmin = 150.0 mm, Dmax = 450.0 mm
Torsion Stress, νst = 2 × T × 106 / (Dmin² × (Dmax - Dmin / 3)) = 0.00 N/mm²
Effective depth, d = 409.0 mm
Shear Stress, νss = V × 1000 / (b × d) = 5.3 × 1000 / (150.0 × 409.0) = 0.09 N/mm²
Part 2 : Clause 2.4.6 and Table 2.3
Maximum Combined Stress Allowed, νtu = Min (0.8 × √fcu, 5) = 4.38 N/mm²
Total Stress, νTot = νss + νst = 0.09 + 0.00 = 0.09 N/mm² ≤ νtu (4.38 N/mm²)
License Number: Timer-SN243-C0-1
4/10
Checking for Combined Stress Allowed Pass
Part 2: Clause 2.4.5
Additional Checking While Small Cross Section (y1 < 550 mm)
Larger Link Dimension, y1 = 390.0 mm < 550 mm
νtu × y1 / 550 = 4.38 × 390.0 / 550 = 3.11 N/mm²
νst = 0.00 N/mm² ≤ 3.11 N/mm²
Checking for Torsion Stress Allowed Pass
Part 2 : Clause 2.4.6 Table 2.3
Torsion Strength contributed by concrete, νt,min = Min (0.067 × √fcu, 0.4) = 0.37 N/mm²
Torsion Stress, νst = 0.00 N/mm² < νt,min = 0.37 N/mm² -> No Torsion Reinforcement is needed
Maximum Shear within Zone, V = 5.0 kN
Maximum Shear Stress Allowed, νMax = Min (0.8 × √30, 5) = 4.38 N/mm² - Clause 3.4.5.2
Shear Stress, νss = V × 1000 / (b × d) = 5.0 × 1000 / (150.0 × 409.0) = 0.08 N/mm² ≤ νMax (4.38 N/mm²)
Checking for Maximum Shear Stress Allowed Pass
Tension Steel Area Provided, Ast = 226 mm²
- Table 3.8: Values of νc, design concrete shear stress
Steel Percentage, 100 × As / (bv × d) = 0.37 % ≤ 3.0 %
Effective Depth Ratio, edr = 400 / d = 400 / 409.0 = 0.978
(400 / d)^ ¼ = 0.994 < 1, (400 / d)^ ¼ taken as 1
Minimum fcu, fcuMin = 25 N/mm², Concrete Grade Ratio, Min(fcu, 40) / fcuMin = 30 / 25 = 1.200
Concrete Shear Capacity, νc = 0.79 {100 As / (bv d)}⅓ (400 / d)¼ (fcu / 25)⅓ / γm
= 0.79 × {0.37}⅓ × 1.000 × (1.200)⅓ / 1.25 = 0.48 N/mm²
Minimum Design Shear Stress, νMin = 0.40 N/mm²
νss = 0.082 < νc + 0.4, Provides only minimum link
Design for minimum Shear Stress, νd = νmin = 0.40 N/mm²
Shear Link Area / Spacing Ratio, SAsv_Sv = (vd × b) / (fyy × fy) = (0.40 × 150) / (0.95 × 460) = 0.137 mm²/mm
Shear Reinforcement Provided : T10-250 (Link spacing is governed by user setting)
Shear Link Area / Spacing Ratio Provided = 0.628 mm²/mm > 0.137 mm²/mm
DEFLECTION CHECKING FOR SPAN
Basic Span / Effective Depth Ratio, Br = 26.0
Span Length, l = 3300.0 mm, Effective Depth, d = 409.0 mm
Actual Span / Effective Depth Ratio, Ar = 8.1
Ultimate Design Moment, Mu = 1.8 kNm
Design Steel Strength, fy = 460.0 N/mm²
Tension Steel Area Required, AsReq = 88 mm²
Tension Steel Area Provided, AsProv = 226 mm²
Compression Steel Area Provided, AsProv (Comp.) = 226 mm²
- Checking for deflection is based on BS8110: 1997
- Table 3.9: Basic span / effective depth ratio for rectangular or flange beams
- Table 3.10: Modification factor for tension reinforcement
- Table 3.11: Modification factor for compression reinforcement
Design Service Stress in Tension Reinforcement, Equation 8
fs = {(2 × fy × AsReq) / (3 × AsProv)} × (1 / ßb)
= {(2 × 460.0 × 88) / (3 × 226)} × (1 / 1.00) = 119.0 N/mm²
Modification Factor for Tension Reinforcement, Equation 7
MFt = 0.55 + {(477 - fs) / (120 × (0.9 + (M/bd²)))}
= 0.55 + {(477 - 119.0) / (120 × (0.9 + (1.8 × 1000000 / (150 × 409.0²)))}
= 3.62 > 2.0
MFt taken as 2.0
License Number: Timer-SN243-C0-1
5/10
New Modification Factor for Compression Reinforcement, Equation 9
MFc = 1 + {(100 × AsProv / (b × d)) / (3 + (100 × AsProv / (b × d)))}
= 1 + {(100 × 226 / (150.0 × 409.0)) / (3 + (100 × 226 / (150.0 × 409.0)))}
= 1.11 <= 1.5
New Deflection Ratio = (Br × MFt × MFc) / Ar = (26.0 × 2.00 × 1.11) / 8.1 = 7.15
Ratio >= 1.0 : Deflection Checked PASSED
BEAM GB4(150x450) SPAN NO. 2
FLEXURAL DESIGN CALCULATION
LOCATION : SPAN
Design Bending Moment = 1.8 kNm Width, b = 150.0 mm Effective Depth, d = 409.0 mm
Mu / bd² = 1.8 × 1000000 / (150.0 × 409.0²) = 0.072 N/mm²
Singly Reinforced Design, limit Mu / bd² < kk1
Mu / bd² = 0.072 <= 4.691
Design as Singly Reinforced Rectangular Beam
Concrete Neutral Axis, x = 2.428 mm
Concrete Compression Force, Fc = k1 × b × x / 1000 = 12.12 × 150 × 2.428 / 1000 = 4.41 kN
Steel Area Required, AsReq = Fc × 1000 / (fy / γs) = 4.41 × 1000 / (460 / 1.05) = 11 mm²
Moment Capacity = Fc × (d - k2 × x) / 1000 = 4.41 × (409.0 - 0.4518 × 2.428) / 1000 = 1.8 kNm
Maximum Depth of Section = 450.0 mm
Minimum Tension Steel Area Required = 0.13% × 150.0 × 450.0 = 88 mm²
Top Compression Steel Area Required = 88 mm²
Bottom Tension Steel Area Required = 88 mm²
Top Reinforcement Provided = 2T12 (226 mm²)
Bottom Reinforcement Provided = 2T12 (226 mm²)
LOCATION : LEFT SUPPORT
Design Bending Moment = 4.5 kNm Width, b = 150.0 mm Effective Depth, d = 409.0 mm
Mu / bd² = 4.5 × 1000000 / (150.0 × 409.0²) = 0.180 N/mm²
Singly Reinforced Design, limit Mu / bd² < kk1
Mu / bd² = 0.180 <= 4.691
Design as Singly Reinforced Rectangular Beam
Concrete Neutral Axis, x = 6.110 mm
Concrete Compression Force, Fc = k1 × b × x / 1000 = 12.12 × 150 × 6.110 / 1000 = 11.11 kN
Steel Area Required, AsReq = Fc × 1000 / (fy / γs) = 11.11 × 1000 / (460 / 1.05) = 26 mm²
Moment Capacity = Fc × (d - k2 × x) / 1000 = 11.11 × (409.0 - 0.4518 × 6.110) / 1000 = 4.5 kNm
Maximum Depth of Section = 450.0 mm
Minimum Tension Steel Area Required = 0.13% × 150.0 × 450.0 = 88 mm²
Top Tension Steel Area Required = 88 mm²
Bottom Compression Steel Area Required = 88 mm²
Top Reinforcement Provided = 2T12 (226 mm²)
Bottom Reinforcement Provided = 2T12 (226 mm²)
LOCATION : RIGHT SUPPORT
Design Bending Moment = 0.0 kNm Width, b = 150.0 mm Effective Depth, d = 409.0 mm
Mu / bd² = 0.0 × 1000000 / (150.0 × 409.0²) = 0.000 N/mm²
Design to minimum steel percentage specified by code,
Maximum Depth of Section = 450.0 mm
Minimum Tension Steel Area Required = 0.13% × 150.0 × 450.0 = 88 mm²
License Number: Timer-SN243-C0-1
6/10
Top Tension Steel Area Required = 88 mm²
Top Reinforcement Provided = 2T12 (226 mm²)
Bottom Reinforcement Provided = 2T12 (226 mm²)
LOCATION : 1/4 SPAN
Design Bending Moment = 1.1 kNm Width, b = 150.0 mm Effective Depth, d = 409.0 mm
Mu / bd² = 1.1 × 1000000 / (150.0 × 409.0²) = 0.044 N/mm²
Singly Reinforced Design, limit Mu / bd² < kk1
Mu / bd² = 0.044 <= 4.691
Design as Singly Reinforced Rectangular Beam
Concrete Neutral Axis, x = 1.484 mm
Concrete Compression Force, Fc = k1 × b × x / 1000 = 12.12 × 150 × 1.484 / 1000 = 2.70 kN
Steel Area Required, AsReq = Fc × 1000 / (fy / γs) = 2.70 × 1000 / (460 / 1.05) = 7 mm²
Moment Capacity = Fc × (d - k2 × x) / 1000 = 2.70 × (409.0 - 0.4518 × 1.484) / 1000 = 1.1 kNm
Maximum Depth of Section = 450.0 mm
Minimum Tension Steel Area Required = 0.13% × 150.0 × 450.0 = 88 mm²
Top Tension Steel Area Required = 88 mm²
Bottom Compression Steel Area Required = 88 mm²
Top Reinforcement Provided = 2T12 (226 mm²)
Bottom Reinforcement Provided = 2T12 (226 mm²)
SHEAR & TORSION DESIGN CALCULATION
LOCATION : SECTION 1 LEFT SUPPORT
(B:0 mm E:825 mm from left grid of span)
Maximum Torsion within Zone, T = 0.0 kNm
Shear at Location of Maximum Torsion, V = 5.3 kN
Link Horizontal Dimension, h1 = b - 2 × Side Cover - DiaLink = 150 - 2 × 25 - 10 = 90 mm
Link Vertical Dimension, v1 = h - 2 × Cover - DiaLink = 450 - 2 × 25 - 10 = 390 mm
Dimension x1 = Min (h1, v1) = 90 mm, y1 = Max (h1, v1) = 390 mm
Section Dimension: Dmin = 150.0 mm, Dmax = 450.0 mm
Torsion Stress, νst = 2 × T × 106 / (Dmin² × (Dmax - Dmin / 3)) = 0.00 N/mm²
Effective depth, d = 409.0 mm
Shear Stress, νss = V × 1000 / (b × d) = 5.3 × 1000 / (150.0 × 409.0) = 0.09 N/mm²
Part 2 : Clause 2.4.6 and Table 2.3
Maximum Combined Stress Allowed, νtu = Min (0.8 × √fcu, 5) = 4.38 N/mm²
Total Stress, νTot = νss + νst = 0.09 + 0.00 = 0.09 N/mm² ≤ νtu (4.38 N/mm²)
Checking for Combined Stress Allowed Pass
Part 2: Clause 2.4.5
Additional Checking While Small Cross Section (y1 < 550 mm)
Larger Link Dimension, y1 = 390.0 mm < 550 mm
νtu × y1 / 550 = 4.38 × 390.0 / 550 = 3.11 N/mm²
νst = 0.00 N/mm² ≤ 3.11 N/mm²
Checking for Torsion Stress Allowed Pass
Part 2 : Clause 2.4.6 Table 2.3
Torsion Strength contributed by concrete, νt,min = Min (0.067 × √fcu, 0.4) = 0.37 N/mm²
Torsion Stress, νst = 0.00 N/mm² < νt,min = 0.37 N/mm² -> No Torsion Reinforcement is needed
Maximum Shear within Zone, V = 5.0 kN
Maximum Shear Stress Allowed, νMax = Min (0.8 × √30, 5) = 4.38 N/mm² - Clause 3.4.5.2
License Number: Timer-SN243-C0-1
7/10
Shear Stress, νss = V × 1000 / (b × d) = 5.0 × 1000 / (150.0 × 409.0) = 0.08 N/mm² ≤ νMax (4.38 N/mm²)
Checking for Maximum Shear Stress Allowed Pass
Tension Steel Area Provided, Ast = 226 mm²
- Table 3.8: Values of νc, design concrete shear stress
Steel Percentage, 100 × As / (bv × d) = 0.37 % ≤ 3.0 %
Effective Depth Ratio, edr = 400 / d = 400 / 409.0 = 0.978
(400 / d)^ ¼ = 0.994 < 1, (400 / d)^ ¼ taken as 1
Minimum fcu, fcuMin = 25 N/mm², Concrete Grade Ratio, Min(fcu, 40) / fcuMin = 30 / 25 = 1.200
Concrete Shear Capacity, νc = 0.79 {100 As / (bv d)}⅓ (400 / d)¼ (fcu / 25)⅓ / γm
= 0.79 × {0.37}⅓ × 1.000 × (1.200)⅓ / 1.25 = 0.48 N/mm²
Minimum Design Shear Stress, νMin = 0.40 N/mm²
νss = 0.082 < νc + 0.4, Provides only minimum link
Design for minimum Shear Stress, νd = νmin = 0.40 N/mm²
Shear Link Area / Spacing Ratio, SAsv_Sv = (vd × b) / (fyy × fy) = (0.40 × 150) / (0.95 × 460) = 0.137 mm²/mm
Shear Reinforcement Provided : T10-250 (Link spacing is governed by user setting)
Shear Link Area / Spacing Ratio Provided = 0.628 mm²/mm > 0.137 mm²/mm
LOCATION : SECTION 1 MIDDLE ZONE
(B:825 mm E:2475 mm from left grid of span)
Maximum Torsion within Zone, T = 0.0 kNm
Shear at Location of Maximum Torsion, V = 2.8 kN
Link Horizontal Dimension, h1 = b - 2 × Side Cover - DiaLink = 150 - 2 × 25 - 10 = 90 mm
Link Vertical Dimension, v1 = h - 2 × Cover - DiaLink = 450 - 2 × 25 - 10 = 390 mm
Dimension x1 = Min (h1, v1) = 90 mm, y1 = Max (h1, v1) = 390 mm
Section Dimension: Dmin = 150.0 mm, Dmax = 450.0 mm
Torsion Stress, νst = 2 × T × 106 / (Dmin² × (Dmax - Dmin / 3)) = 0.00 N/mm²
Effective depth, d = 409.0 mm
Shear Stress, νss = V × 1000 / (b × d) = 2.8 × 1000 / (150.0 × 409.0) = 0.05 N/mm²
Part 2 : Clause 2.4.6 and Table 2.3
Maximum Combined Stress Allowed, νtu = Min (0.8 × √fcu, 5) = 4.38 N/mm²
Total Stress, νTot = νss + νst = 0.05 + 0.00 = 0.05 N/mm² ≤ νtu (4.38 N/mm²)
Checking for Combined Stress Allowed Pass
Part 2: Clause 2.4.5
Additional Checking While Small Cross Section (y1 < 550 mm)
Larger Link Dimension, y1 = 390.0 mm < 550 mm
νtu × y1 / 550 = 4.38 × 390.0 / 550 = 3.11 N/mm²
νst = 0.00 N/mm² ≤ 3.11 N/mm²
Checking for Torsion Stress Allowed Pass
Part 2 : Clause 2.4.6 Table 2.3
Torsion Strength contributed by concrete, νt,min = Min (0.067 × √fcu, 0.4) = 0.37 N/mm²
Torsion Stress, νst = 0.00 N/mm² < νt,min = 0.37 N/mm² -> No Torsion Reinforcement is needed
Maximum Shear within Zone, V = 2.8 kN
Maximum Shear Stress Allowed, νMax = Min (0.8 × √30, 5) = 4.38 N/mm² - Clause 3.4.5.2
Shear Stress, νss = V × 1000 / (b × d) = 2.8 × 1000 / (150.0 × 409.0) = 0.05 N/mm² ≤ νMax (4.38 N/mm²)
Checking for Maximum Shear Stress Allowed Pass
Tension Steel Area Provided, Ast = 226 mm²
- Table 3.8: Values of νc, design concrete shear stress
Steel Percentage, 100 × As / (bv × d) = 0.37 % ≤ 3.0 %
Effective Depth Ratio, edr = 400 / d = 400 / 409.0 = 0.978
(400 / d)^ ¼ = 0.994 < 1, (400 / d)^ ¼ taken as 1
License Number: Timer-SN243-C0-1
8/10
Minimum fcu, fcuMin = 25 N/mm², Concrete Grade Ratio, Min(fcu, 40) / fcuMin = 30 / 25 = 1.200
Concrete Shear Capacity, νc = 0.79 {100 As / (bv d)}⅓ (400 / d)¼ (fcu / 25)⅓ / γm
= 0.79 × {0.37}⅓ × 1.000 × (1.200)⅓ / 1.25 = 0.48 N/mm²
Minimum Design Shear Stress, νMin = 0.40 N/mm²
νss = 0.045 < νc + 0.4, Provides only minimum link
Design for minimum Shear Stress, νd = νmin = 0.40 N/mm²
Shear Link Area / Spacing Ratio, SAsv_Sv = (vd × b) / (fyy × fy) = (0.40 × 150) / (0.95 × 460) = 0.137 mm²/mm
Shear Reinforcement Provided : T10-250 (Link spacing is governed by user setting)
Shear Link Area / Spacing Ratio Provided = 0.628 mm²/mm > 0.137 mm²/mm
LOCATION : SECTION 1 RIGHT SUPPORT
(B:2475 mm E:3300 mm from left grid of span)
Maximum Torsion within Zone, T = 0.0 kNm
Shear at Location of Maximum Torsion, V = 2.9 kN
Link Horizontal Dimension, h1 = b - 2 × Side Cover - DiaLink = 150 - 2 × 25 - 10 = 90 mm
Link Vertical Dimension, v1 = h - 2 × Cover - DiaLink = 450 - 2 × 25 - 10 = 390 mm
Dimension x1 = Min (h1, v1) = 90 mm, y1 = Max (h1, v1) = 390 mm
Section Dimension: Dmin = 150.0 mm, Dmax = 450.0 mm
Torsion Stress, νst = 2 × T × 106 / (Dmin² × (Dmax - Dmin / 3)) = 0.00 N/mm²
Effective depth, d = 409.0 mm
Shear Stress, νss = V × 1000 / (b × d) = 2.9 × 1000 / (150.0 × 409.0) = 0.05 N/mm²
Part 2 : Clause 2.4.6 and Table 2.3
Maximum Combined Stress Allowed, νtu = Min (0.8 × √fcu, 5) = 4.38 N/mm²
Total Stress, νTot = νss + νst = 0.05 + 0.00 = 0.05 N/mm² ≤ νtu (4.38 N/mm²)
Checking for Combined Stress Allowed Pass
Part 2: Clause 2.4.5
Additional Checking While Small Cross Section (y1 < 550 mm)
Larger Link Dimension, y1 = 390.0 mm < 550 mm
νtu × y1 / 550 = 4.38 × 390.0 / 550 = 3.11 N/mm²
νst = 0.00 N/mm² ≤ 3.11 N/mm²
Checking for Torsion Stress Allowed Pass
Part 2 : Clause 2.4.6 Table 2.3
Torsion Strength contributed by concrete, νt,min = Min (0.067 × √fcu, 0.4) = 0.37 N/mm²
Torsion Stress, νst = 0.00 N/mm² < νt,min = 0.37 N/mm² -> No Torsion Reinforcement is needed
Maximum Shear within Zone, V = 2.6 kN
Maximum Shear Stress Allowed, νMax = Min (0.8 × √30, 5) = 4.38 N/mm² - Clause 3.4.5.2
Shear Stress, νss = V × 1000 / (b × d) = 2.6 × 1000 / (150.0 × 409.0) = 0.04 N/mm² ≤ νMax (4.38 N/mm²)
Checking for Maximum Shear Stress Allowed Pass
Tension Steel Area Provided, Ast = 226 mm²
- Table 3.8: Values of νc, design concrete shear stress
Steel Percentage, 100 × As / (bv × d) = 0.37 % ≤ 3.0 %
Effective Depth Ratio, edr = 400 / d = 400 / 409.0 = 0.978
(400 / d)^ ¼ = 0.994 < 1, (400 / d)^ ¼ taken as 1
Minimum fcu, fcuMin = 25 N/mm², Concrete Grade Ratio, Min(fcu, 40) / fcuMin = 30 / 25 = 1.200
Concrete Shear Capacity, νc = 0.79 {100 As / (bv d)}⅓ (400 / d)¼ (fcu / 25)⅓ / γm
= 0.79 × {0.37}⅓ × 1.000 × (1.200)⅓ / 1.25 = 0.48 N/mm²
Minimum Design Shear Stress, νMin = 0.40 N/mm²
νss = 0.043 < νc + 0.4, Provides only minimum link
Design for minimum Shear Stress, νd = νmin = 0.40 N/mm²
Shear Link Area / Spacing Ratio, SAsv_Sv = (vd × b) / (fyy × fy) = (0.40 × 150) / (0.95 × 460) = 0.137 mm²/mm
License Number: Timer-SN243-C0-1
9/10
Shear Reinforcement Provided : T10-250 (Link spacing is governed by user setting)
Shear Link Area / Spacing Ratio Provided = 0.628 mm²/mm > 0.137 mm²/mm
DEFLECTION CHECKING FOR SPAN
Basic Span / Effective Depth Ratio, Br = 26.0
Span Length, l = 3300.0 mm, Effective Depth, d = 409.0 mm
Actual Span / Effective Depth Ratio, Ar = 8.1
Ultimate Design Moment, Mu = 1.8 kNm
Design Steel Strength, fy = 460.0 N/mm²
Tension Steel Area Required, AsReq = 88 mm²
Tension Steel Area Provided, AsProv = 226 mm²
Compression Steel Area Provided, AsProv (Comp.) = 226 mm²
- Checking for deflection is based on BS8110: 1997
- Table 3.9: Basic span / effective depth ratio for rectangular or flange beams
- Table 3.10: Modification factor for tension reinforcement
- Table 3.11: Modification factor for compression reinforcement
Design Service Stress in Tension Reinforcement, Equation 8
fs = {(2 × fy × AsReq) / (3 × AsProv)} × (1 / ßb)
= {(2 × 460.0 × 88) / (3 × 226)} × (1 / 1.00) = 119.0 N/mm²
Modification Factor for Tension Reinforcement, Equation 7
MFt = 0.55 + {(477 - fs) / (120 × (0.9 + (M/bd²)))}
= 0.55 + {(477 - 119.0) / (120 × (0.9 + (1.8 × 1000000 / (150 × 409.0²)))}
= 3.62 > 2.0
MFt taken as 2.0
New Modification Factor for Compression Reinforcement, Equation 9
MFc = 1 + {(100 × AsProv / (b × d)) / (3 + (100 × AsProv / (b × d)))}
= 1 + {(100 × 226 / (150.0 × 409.0)) / (3 + (100 × 226 / (150.0 × 409.0)))}
= 1.11 <= 1.5
New Deflection Ratio = (Br × MFt × MFc) / Ar = (26.0 × 2.00 × 1.11) / 8.1 = 7.15
Ratio >= 1.0 : Deflection Checked PASSED
BEAM SUPPORT REACTION TABLE
Current Beam Grid Mark: B1A/1A1-2A1
Beam Support Reactions
Support Reaction, kN
Support No. Grid Mark Support Type
Dead Load Live Load
1 1A1 Beam 1.7 0.0
2 2 Beam 7.2 0.0
3 2A1 Beam 1.7 0.0
License Number: Timer-SN243-C0-1
10/10
