Design Procedure of Beams

 Design Procedure (Continuous Beams) 1) Estimate of loading consist of dead load and live load For rectangular slabs that supported in 4-sides, the following method can be used: One-way slab (L/Lx > 2.0)

2

where n = uniform distributed load on slab (kN/m )

Two-way slab (L/Lx < 2.0)

2) Structural analysis – determine the shear and bending moment diagram BS8110: Part 1; Clause 3.4.3

Table 3.5 may be used to calculate the design ultimate bending moments and shear forces, subject to the following provisions: a) characteristic imposed load Qk may not exceed characteristic dead load Gk; b) loads should be substantially uniformly distributed distri buted over three or more spans; c) variations in span length should not exceed 15 % of longest.

If Table 3.5 cannot be used, three cases of loading should be analyzed to determine the envelope of SFD and BMD.

The critical loading arrangements (clause 3.2.1.2.2) which should be considered are as follows: a)

All spans loaded with the maximum design ultimate load (1.4 Gk + 1.6 Qk)

Load case I

b)

Alternate spans loaded with the maximum design ultimate load (1.4 Gk + 1.6 Qk) and other spans loaded with the minimum mi nimum design ultimate load (1.0Gk)

Load case II

Load case III

Case 1

Case III

Case II

Bending Moment and Shear Force Envelopes

3) Design for RC (main reinforcement) to calculate the amount of area required to resist the bending moment.

Design Procedure (Section Design For Moment):  fcubd2 1. Calculate K = M  /   /  fcubd2 2. Check K : ≤ K’ design as singly reinforced section ( K’ = 0.156) (Since k < 0.156, compression reinforcement is not required)

> K’ design as doubly reinforced section Singly Reinforced Section Design: 1. Calculate z = d [ 0.5 + √(0.25 – K  /  / 0.9)]. If  K  K ≤ 0.043 then z = 0.95d  2. Calculate As = M  /  / 0.95 fyz Doubly Reinforced Section Design: 1. Calculate z = d [ 0.5 + √(0.25 – K  /  / 0.9)] 2. Calculate x = (d  –   – z) / 0.45  x: 3. Check d’  /   /  x

≤ 0.43 continue on to stage 4

> 0.43 compression reinforcement elastic  fcubd2 / 0.95 fy(d  – d’  4. Calculate As’ = (K  –   –  K’   K’ ) fcubd2  – d’ ) 5. Calculate As = K’fcubd2 / 0.95 fyz + As’  Choosing Reinforcement: Select the number & diameter of bars to provide an area not less than, and as close as  As and As’ . practicable to, the calculated values of  As Specific Detailing Requirements: Check these requirements are met: 1. Min & max areas of rebar.

2. Number of bars in a bundle ≤ 4. 3. Spacing between bars.

Bar Area Tables

4) Design for shear reinforcement which check on the capacity of shear in RC Design Procedure (Section Design For Shear): Design Procedure:

1. At the given section calculate the shear stress, v: v = V  /   / bvd  Check  v ≤ 0.8√ fcu or 5 N/mm2 2. Calculate the design concrete shear stress, vc, from: vc = 0.79( fcu  fcu /25)1/3 (100 As / bvd  bvd )1/3(400/  d )1/4/  )1/3(400/ d  )1/4/ γm Where: bvd ≤ 3 100 As / bvd  d ≥ 1 400/ d   fcu /25 ≥ 1 and fcu ≤ 40 N/mm2 3. Enhance the design concrete shear capacity for sections ≤ 2d to the support: av enhanced vc = 2vcd   / av 4. Calculate the required area of vertical shear links  Asv, from:  Asv = bvsv(v – vc)/0.95 fy Or calculate the maximum spacing for a given bar size (or  Asv) from: sv = 0.95 fy Asv / bv(v – vc) Choosing Reinforcement:

T or R bars may be used. Usual bar sizes are 8, 10, 12 φ. Link spacing, sv, should be a multiple of 25 mm. Use the same bar size in a beam, just alter the spacing to accommodate accommodate differing strength requirements. Links can be provided across the full width of the beam, they do not have to be concentrated in the perimeter. Specific Detailing Requirements:

Minimum area of shear links to be provided anywhere in a beam:  Asv = 0.4bvsv / 0.95 fy. Spacing of links ≤ 0.75d. Spacing of links should not be less than 100 mm, or 75 mm in exceptional circumstances for poker access to the concrete.

5) Check cracking, deflection and provide detail following the design result.