Deflection check (beam and slab: EC2)
The deflection of reinforced concrete beams is not directly calculated and the serviceability of the beam is measured by comparing the calculated limiting span/effective depth ratio L/d to the maximum allowable values as given by;1
IF ρ ≤ ρ0
(L/d)max = Kss*f1*f2*(11+1.5*(fck) 1/2*(ρ0/ρ)+3.2*(fck)1/2*(( ρ0/ρ)-1)3/2)*(500*Ast,prov/(fyk*A st,reqd))
IF ρ > ρ0
(L/d)max = Kss*f1*f2*(11+1.5*(fck) 1/2*(ρ0/(ρ-ρ'))+(1/12)*(fck)1/2*( ρ'/ρ0)1/2)*(500*Ast,prov/(fyk*A st,reqd))
where
ρ |
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the designed tension reinforcement ratio at mid-span (or at support for cantilevers) required to resist bending |
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A st.reqd /(b w *d) for rectangular beams | |
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A st,reqd /(b eff *d) for flanged beams | |
ρ' |
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the designed compression reinforcement ratio at mid-span (or at support for cantilevers) required to resist bending |
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A s2,reqd /(b w *d) for rectangular beams | |
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A s2,reqd /(b eff *d) for flanged beams | |
A st,reqd |
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the designed area of tension reinforcement at mid-span (or at support for cantilevers) required to resist bending |
A st,prov |
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MIN(the area of tension reinforcement provided at mid-span (or at support for cantilevers), f 3 *A st,reqd ) |
A s2,reqd |
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the designed area of compression reinforcement at mid-span (or at support for cantilevers) required to resist bending |
f 1 |
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f 2 |
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7/L eff IF L eff > 7 m with L eff in metre units | |
L eff |
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the length of the beam between the centre of its supports2 |
f 3 |
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an NDP factor as given below |
K ss |
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the structural system factor which is an NDP and is given below |
For design in accordance with EC2 Recommendations the NDP value of f3 is given by3;
f3 = 1.5
For design in accordance with UK NA, Irish NA, Malaysian NA and Singapore NA the NDP value of f3 is given by4;
f3 = 1.5
For design in accordance with UK NA, EC2 Recommendations, Irish NA, Malaysian NA and Singapore NA the NDP value of Kss is given by the following table:
Span Detail | LH End Fixity | RH End Fixity | Kss |
---|---|---|---|
LH End Span | Fixed | Fixed | 1.3 |
Fixed | Pinned | 1.0 | |
Pinned | Fixed | 1.3 | |
Pinned | Pinned | 1.0 | |
Internal Span | Fixed | Fixed | 1.5 |
Fixed | Pinned | 1.3 | |
Pinned | Fixed | 1.3 | |
Pinned | Pinned | 1.0 | |
RH End Span | Fixed | Fixed | 1.3 |
Fixed | Pinned | 1.3 | |
Pinned | Fixed | 1.0 | |
Pinned | Pinned | 1.0 | |
Cantilever | 0.4 |