14--Prof. Zahid Ahmad Siddiqi Lec-14-Design of Beams

Plain & Reinforced Concrete-1 CE-314

Sixth Term Civil Engineering

Lecture # 14

Flexural Analysis and Design of Beams

(Ultimate Strength Design of Beams)

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Prof. Prof. Dr. Zahid Zahid Ahmad Siddiqi Siddiqi

DESIGN OF DOUBLY REINFORCED SECTIONS 



Data:

i) Loads and span length ii) f c ′ , f y and E s iii) Architectural depth restriction Required: i) Beam cross-sectional dimensions such as b d d ′ ′ and h














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

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Calculate all types of loads acting on the structure and hence calculate the total factored load. Calculate the total maximum factored moment, M u, acting on the member. Also decide the tentative cross-sectional dimensions of the member. Calculate minimum effective depth required for singly reinforced section.














d min 



=

M u 0.205 f c′b

Calculate the maximum moment that can be resisted by the tension-steel according to the maximum steel ratio for singly reinforced section for an extreme tensile strain of 0.005. ρ = ρ max

= 0.85

× 0.375 β 1

f ′c f













Prof. Prof. Dr. Zahid Zahid Ahmad Siddiqi Siddiqi 



In the above expressions, M 1 is the moment capacity provided by the maximum compression in the concrete and A and As1 is the area of tension steel to balance the maximum compression developed in the concrete according to the code allowed value of extreme tensile strain. Calculate the excess moment (M ( M 2) that must be resisted by the moment capacity provided by the compression in the compression steel. M 2

= M u − M 1














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The total amount of tension steel may be calculated by adding an extra amount of tension steel equal to the above required compression steel in to the already calculated tension steel. As2 = As′ As = As1 + As2 Calculate the tensile steel ratio and check for yielding of compression steel by any















Prof. Prof. Dr. Zahid Zahid Ahmad Siddiqi Siddiqi 



If ρ ≥ ρ cy, compr compres essio sion n steel steel is yield yieldin ing, g, as as assumed be before an and amount of of compression steel = As′ If the steel ratio ( ρ ) is lesser than (compression steel is not yielding), stress in














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If the compression steel is not yielding, compression steel area ( As′) is increased to














Example 4.2: Design a simply supported rectangular beam having a span of 6m, subjected to a total factored load including the self weight of 70 kN/m. The depth of the beam should not exceed its span over














Solution:   

= 6m w u = 70 kN/m b = 300 mm l
















hsel

= 500 mm



d = hsel − 75 = 425 mm
















Case (i)


























′

0 003

c − d ′


0 003

125 − 58



























300








































































































































Plain & Reinforced Concrete-1 Tf A sf f y A sf

= C f

= 0.85f c ' ( b − b w )β1h f

= 0.85β1h f Tw

f c ' f y

( b − b w )

= Cw

(A s − A sf )f y = 0.85f c ' b w a

Only for case-III














Plain & Reinforced Concrete-1 Flexural Capacity From Compression Side

Mn

= Mnf + Mnw

β1h f  a    Mn = Cf  d −  + Cw  d −  2    2 














Plain & Reinforced Concrete-1 Flexural Capacity From Tension Side

Mn

= Mnf + Mnw

β1h f  a    Mn = Tf  d −  + Tw  d −  2    2 














Plain & Reinforced Concrete-1 Tension Controlled Failure of T-Beam ρw ρ f

= =

ρ b =

As b w d A sf

= Total tension steel area (all steel will be in web)

= Steel ratio to balance the flange compressive force

b w d Balanced steel ratio for the singly reinforced rectangular section














Plain & Reinforced Concrete-1 For longitudinal equilibrium

= C w + C f T = C w + Tf

T

A s f y Divide by fybwd

= 0 .85 f c ' bw a + A sf f y l
















Plain & Reinforced Concrete-1 For longitudinal equilibrium For εst = 0.005

al

3

= β1 × d 8

To ensure tension controlled c ontrolled section














Plain & Reinforced Concrete-1 Capacity Analysis Known:

b, d, bw, hf, L, fc’, fy, As

Required: φ M














Plain & Reinforced Concrete-1 Capacity Analysis (contd…) If c > hf Beam is to be designed as T-Beam














Plain & Reinforced Concrete-1 Capacity Analysis (contd…) Step # 6

Calculate εs and φ factor














Plain & Reinforced Concrete-1 Example: A T-Beam has the following data:















Solution:















A

= A

A

= 3900

1935 = 1965 mm2














Case (ii)














14--Prof. Zahid Ahmad Siddiqi Lec-14-Design of Beams

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