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Prestress Concrete Design Sessional

ULTIMATE STRENGTH DESIGNT BEAM DESIGN : Singly and Doubly

CE 416

Presented ByS. M. Rahat Rahman

10.01.03.044

Contents

Ultimate Strength Design

▫ USD (ultimate strength design)

▫ Assumption of USD

▫ Singly and Doubly Reinforced Beam

▫ T - Beam design

Ultimate Strength Design ( T BEAM ) || an introduction

Ultimat Strength Design

▫ Method of the determine the dimension of structure based on

▫ Ultimate load▫ Ultimate section

Ultimate Strength Design

▫ Historical BackgroundBeing used since 1957.

Ultimate Strength Design

▫ AssumptionsAssumptions simplify analysis.

Ultimate Strength Design || Assumption

Assumptions• Bars at the same level, provided that the

bond between the concrete and steel is adequate

• Is linearly proportional to the distance from the neutral axis.

• Modulus of elasticity for all grades of steel is taken as Es = 29 x 10 ^ 6 psi

Ultimate Strength Design || Assumption

Assumptions

• Plane cross sections continue to be plane after bending

• Concrete's tensile strength is about 1/10 of its compressive strength

• Cracked concrete is assumed to be not effective before cracking, the entire cross section is effective in resisting the external moments

Ultimate Strength Design || Assumption

Assumptions

• At high stresses, non-elastic behavior is assumed, which is in close agreement with the actual behavior of concrete and steel

• Maximum strain at the extreme compression fibers 0.003 by ACI code

• Compressive stress distribution may be assumed to be rectangular, parabolic or trapezoidal.

Ultimate Stress Design || Advantages

Advantages

▫ Better predicts strength

▫ Requires lesser material

▫ Easier to compute

▫ More rational approach

▫ Accounts for uncertainties in load.

Ultimate Strength Design

Beam Types

▫ Singly reinforced section

▫ Doubly reinforced section

▫ T-section

n w

Ultimate Strength Design

designing beam .. .

Ultimate Stress Design

▫ Singly Reinforced BeamA singly reinforced beam is one in which the concrete element is only reinforced near the tensile face and the reinforcement, called tension steel, is designed to resist the tension.

Ultimate Strength Design

▫ Doubly Reinforced BeamA doubly reinforced beam is one in which besides the tensile

reinforcement the concrete element is also reinforced near the compressive face to help the concrete resist compression. The latter reinforcement is called compression steel. When the compression zone of a concrete is inadequate to resist the compressive moment (positive moment), extra reinforcement has to be provided if the architect limits the dimensions of the section.

Ultimate Strength Design

▫ T-Section

T BEAM For monolithically casted slabs, a part of a slab act as a part of beam to resist longitudinal compressive force in the moment zone and form a T-Section.

Ultimate Strength Design

▫ T-SectionFrom ACI 318, Section 8.10.2

Effective Flange Width : Condition 1

For symmetrical T-Beam or having slab on both sides a) 16 hf + bw b) Span/4 c) c/c distance (smallest value should be taken)

▫ T-SectionFrom ACI 318, Section 8.10.2

Effective Flange Width : Condition 2 Beams having slabs on one side only a) bw + span/12 b) bw + 6hf c) bw + 1/2 * beam clear distance (smallest value should be taken)

▫ T-SectionFrom ACI 318, Section 8.10.2

Effective Flange Width :Condition 3

Isolated T Beam

a) beff ≤ 4 bw b) hf ≥ bw/2 (smallest value should be taken)

Ultimate Stress Design || T-section

T-Section basics

Ultimate Stress Design || T-section

T-Section behaviours

▫ T-section behaving as

▫ Rectangular section

▫ T-section

Continuous T-Beam

T- versus Rectangular Sections

When T-shaped sections are subjected to negative bending moments, the flange is located in the tension zone. Since concrete strength in tension is usually neglected in strength design, the sections are treated as rectangular sections of width w b . On the other hand, when sections are subjected to positive bending moments, the flange is located in the compression zone and the section is treated as a T-section shown in Figure 1

Continuous T-Beam

Continuous T-Beam

T - Section design

Strength Analysis :

1st case : (N.A. is with in the flange)

Analyze as a rectangular beam of width b = beff

Mn = As fy (d − a/2)

T-Section design

Case 2 : (N. A. is with in the web)

T beam may be treated as a rectangular if stress block depth a ≤ hf and as a T beam If a > hf .

Analysis of T-Beam

26

Case 1:

Equilibriumfha

s y

c eff0.85

A fT C a

f b

Analysis of T-Beam

27

Case 1:

Confirm

fha

005.0cus

1

ys

c

cd

ac

Analysis of T-Beam

28

Case 1:

Calculate Mn

fha

2ysn

adfAM

Analysis of T-Beam

29

Case 2: Assume steel yields fha

ys

wcw

fwcf

85.0

85.0

fAT

abfC

hbbfC

Analysis of T-Beam

30

Case 2: Equilibrium

Assume steel yields

fha

c w fsf

y

0.85 f b b hA

f

The flanges are considered to be equivalent compression steel.

s sf yf w

c w0.85

A A fT C C a

f b

Analysis of T-Beam

31

Case 2:

Confirm

fha

f

1

s cu 0.005

a h

ac

d c

c

Analysis of T-Beam

32

Case 2:

Calculate nominal moments

fha

n n1 n2

n1 s sf y

fn2 sf y

2

2

M M M

aM A A f d

hM A f d

Analysis of T-Beams

33

The definition of Mn1 and Mn2 for the T-Beam are given as:

Limitations on Reinforcement for Flange Beams

• Lower Limits– Positive Reinforcement

34

c

ysmin

w

y

4 larger of

1.4

f

fA

b d

f

Limitations on Reinforcement for Flange Beams

• Lower Limits– For negative reinforcement and T

sections with flanges in tension

35

c

y(min)

y

2 larger of

1.4

f

f

f

Ultimate Stress Design || T-section

T-Section design

Thank you