SPONSORED
Sample calculation for deflection checking based on BS 8110: 1997
Please take note that checking for deflection is based on BS8110: 1997 by refer to ;
a) Table 3.9: Basic span / effective depth ratio for rectangular or flange beams
b) Table 3.10: Modification factor for tension reinforcement
c) Table 3.11: Modification factor for compression reinforcement
Deflection checking for span
Basic Span / Depth Ratio, Br = 20.0
Span Length, l = 5000.0 mm
Effective Depth, d = 445.0 mm
Actual Span / Depth Ratio, Ar = 11.2
Ultimate Design Moment, Mu = 73.5 kNm
Design Steel Strength, fy = 460.0 N/mm²
Area of Tension Steel Required, AsReq = 432 mm²
Area of Tension Steel Provided, AsProv = 628 mm²
Area of Compression Steel Provided, AsProv (Comp.) = 157 mm²
Design Service Stress in Tension Reinforcement, Equation 8
fs = {(2 × fy × AsReq) / (3 × AsProv)} × (1 / ßb)
= {(2 × 460.0 × 432) / (3 × 628)} × (1 / 1.00)
= 210.7 N/mm²
Modification Factor for Tension Reinforcement, Equation 7
MFt = 0.55 + {(477 - fs) / (120 × (0.9 + (M/bd²)))}
= 0.55 + {(477 - 210.7) / (120 × (0.9 + (73.5 × 1000000 / (150 × 445.0²)))}
= 1.21
New Modification Factor for Compression Reinforcement, Equation 9
MFc = 1 + {(100 × AsProv / (b × d)) / (3 + (100 × AsProv / (b × d)))}
= 1 + {(100 × 157 / (150.0 × 445.0)) / (3 + (100 × 157 / (150.0 × 445.0)))}
= 1.07
Deflection Ratio = (Br × MFt × MFc) / Ar = (20.0 × 1.21 × 1.07) / 11.2 = 2.31
Ratio 2.31 higher than 1.0, therefore ;
Deflection checking is pass !
