## Flanged beams

Flanged beams can be treated in much the same way as in BS 8110. The main differences compared with BS 8110 are that the assessment of the flange width is more sophisticated (see Figures 9 and 10) and that Eurocode 2 contains a check to confirm that the shear stress at

Continues page 31

Figure 6

Procedure for assessing deflection

 H Determine basic l/d and K from Figure 7

Determine Factor 1 (F1) For ribbed or waffle slabs F1 = 1 - 0.1 ((fcf/fcw) - 1) 2 0.8+ (bf is flange breadth and bw is rib breadth) Otherwise F1 = 1.0

Determine Factor 2 (F2) Where the slab span exceeds 7 m and it supports brittle partitions, F2 = 7/ieff < 1.0 Otherwise F2 = 1.0

Where os = Stress in reinforcement at serviceability limit state (see Figure 8) 0*5 may assumed to be 310 MPa (i.e. F3 = 1.0) Note: As,prov < 1.5 -As req'd (UK National Annex)

+ The Eurocode is ambiguous regarding linear interpolation. It is understood that it was the intention of the drafting committee that linear interpolation be used and this is in line with current UK practice.

Figure 8

Determination of steel stress

320 300

rf 280

IS 260

Tu 240

t5 o

E 220

200 180

i

' i

i

 C2 = 0.8, Yc = 1.35 - C2 = 0.6, Yc = 1.25 C2 = 0.6, Yc = 1.35 - C2 = 0.3, Yc = 1.25 C2 = 0.3, Yc = 1.35 C2 = 0.2, Yc = 1.25 C2 = 0.2, Yc = 1.35

To determine stress in the reinforcement (os), calculate the ratio Gk/Qk, read up the graph to the appropriate curve and read across to determine osu.

os can be calculated from the expression: os = osu ( As,req ) (—)

Figure 7

Basic span-to-effective-depth ratios

36 34 32 30 28

IT 26

c ro

0.40% 0.60% 0.80% 1.00% 1.20% 1.40% 1.60% Percentage of tension reinforcement (ASireq'd/bd)

Notes

1 This graph assumes simply supported span condition (K = 1.0).

K =1.5 for interior span condition K =1.3 for end span condition K = 0.4 for cantilevers.

2 Compression reinforcement, p, has been taken as 0.

3 Curves based on the following expressions:

Figure 11

Procedure for determining flexural capacity of flanged beams

START

Carry out analysis of beam to determine design moments, M (see Table 3)

Determine lo (see Figure 9) and beff from: beff = (bw+ beff1 + beff2) where beffi = (0.2bi + 0.1 lo) < 0.2 lo < bi beff2 = (0.2b2 + 0.1 lo) < 0.2 lo < b2 Note: The flange width at the support will be different from that at mid-span. For symbols refer to Figures 9 and 10

Determine K from K =

where b = bw at support b = beff in span bd2 fck

Determine K' from Table 4 or K' = 0.60 d - 0.18 ô2 - 0.21 where d < 1.0

 Calculate lever arm z f z = 2 [ 1+V1 - 3.53K rom < 0.95d Calculate depth to neutral axis x from: x = 2.5 (d - z) Is x < 1 No ^^ Yes .25hf ? ^-

Neutral axis in flange. Design as rectangular section (Figure 2) and then check longitudinal shear (Figure 14)

Neutral axis in web Calculate moment capacity of flange from:

 Is Kf - k '? Redesign section Yes Calculate area of reinforcement required from MR,f M - MR,f ^ = i S /ywd(d - 0.5 f fywd Check longitudinal shear (see Figure 14)

Figure 9

Definition of lo, for calculation of effective flange width

 l0 = 0.85 l1 l0 = 0.15 (li + I2 ) l0 = 0.7 I2 l0 = 0.15 I2 + I3 Effective flange width parameters Figure 10 Effective flange width parameters Figure 12 Placing of tension reinforcement in flanged cross section Figure 12 Placing of tension reinforcement in flanged cross section Figure 13 Notations for the connection between flange and web Figure 13 Notations for the connection between flange and web the interface of the fiange and web can be resisted by the transverse reinforcement in the fiange. The position of the neutral axis should be determined, and then the area of reinforcement can be calculated depending whether it lies in the flange or web (see Figure 11). At supports the tension reinforcement to resist hogging moments should be distributed across the full width of the effective flange as shown in Figure 12.The span-to-depth deflection checks using ratio of tension reinforcement should be based on area of concrete above centre of tension steel.

0 0

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### Responses

• katrin lehmann
How to support cantilever structures in concrete structures?
8 years ago
• Cesar
Why is transverse reinforcement used in flange beams?
7 years ago
• marzio
Why the flange factor is used in concrete eurocode 2 for deflection?
3 years ago
• joe
How to check flanged beams according to eurocode?
3 years ago