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Design of Concrete Structure I

University of Palestine

بسم الله الرحمن الرحيم

Chapter 5

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 1

Shear and Diagonal Tension in Beam

Introduction

Loads applied to beams produce bending moments, shearing forces, as

shown in Figure, and in some cases torques.

Moment is usually considered first; leading to cross sectional dimensions and the longitudinal reinforcement. The section is then checked for shear to determine whether shear reinforcement is required or not.

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 2

Shear and Diagonal Tension in Beam

Introduction

Shear failure of reinforced concrete, more properly called diagonal tension failure. Shear failure is difficult to predict accurately and it is likely to occur suddenly, with no advanced warning. This is in strong contrast with the nature of flexural failure.

RC beams are generally provided with special shear reinforcement to ensure that flexural failure would occur before shear failure if the member should be severely overloaded.

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 3

Shear and Diagonal Tension in Beam

Diagonal Tension in Homogeneous Elastic beam

The equations of the shear stress and flexural (normal) stress at any point in the section, located at a distance y from the neutral axis, are given as

A0

Shear stress

distribution

Bending stress

distribution

Cross section

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Shear stress

distribution

Cross section

Page 4

Shear and Diagonal Tension in Beam

Diagonal Tension in Homogeneous Elastic beam

Note: The maximum 1st moment

occurs at the neutral axis (NA).

A0

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

2

0

1

Page 5

Shear and Diagonal Tension in Beam

Diagonal Tension in Homogeneous Elastic beam

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

f2 = fc

f1 = ft

α

fc

ft

Tension trajectories

Compression trajectories

Principle stress trajectories

Page 6

Shear and Diagonal Tension in Beam

Diagonal Tension in Homogeneous Elastic beam

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 8

Shear and Diagonal Tension in Beam

Types of Shear Cracks

Two types of inclined cracking occur in beams:

1- Web Shear Cracks

Web shear cracking begins from an interior point in a member at the level of the centroid of uncracked section and moves on a diagonal path to the tension face when the diagonal tensile stresses produced by shear exceed the tensile strength of concrete.

2- Flexure-Shear Cracks

The most common type, develops from the tip of a flexural crack at the tension side of the beam and propagates towards mid depth until it is checked on the compression side of the beam.

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 8

Shear and Diagonal Tension in Beam

Cracks in Beams

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 9

Shear and Diagonal Tension in Beam

Designing to Resist Shear

According to ACI Code, the design of beam for shear is to be based on the relation

Vu = factored shear force at section

Vn = nominal shear strength

Φ = strength reduction factor for shear = 0.75

The nominal shear force is generally resisted by concrete and shear reinforcement or,

Vc = nominal shear force resisted by concrete

Vs = nominal shear force resisted by shear reinforcement

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 10

Shear and Diagonal Tension in Beam

Strength of Concrete in Shear

For members subject to shear and bending only, ACI Code gives the following equation for evaluating Vc

A more exact formula is specified by ACI Code, given by the following equation

should not exceed 1.0

Simple formula

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 11

Shear and Diagonal Tension in Beam

Strength of Concrete in Shear

For members subject to axial compression plus shear,ACI Code gives the following equation for evaluating Vc

For members subject to axial tension plus shear, ACI Code gives the following equation for evaluating Vc

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 12

Shear and Diagonal Tension in Beam

Types of Shear Reinforcement

- The code allows the use of three types of Shear Reinforcement
- Vertical Stirrups
- Inclined stirrups
- Bent up bars

Vertical Stirrups

Inclined Stirrups

Bent up bars

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 13

Shear and Diagonal Tension in Beam

Shear Resisted by stirrups

Shear reinforcement required when

Vs= T sinα

T = n Av fys

n = s/s1 , where s1 = d (cot α+ cot 45)

For vertical stirrups,

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 14

Shear and Diagonal Tension in Beam

Minimum Amount of Shear Reinforcement

Minimum Shear Reinforcement (Av,min) required when

Maximum Stirrup Spacing

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 15

Shear and Diagonal Tension in Beam

Ensuring Ductile Behavior

ACI Code requires that the maximum force resisted by shear

reinforcement Vs is not to exceed

Anchorage of Stirrups

Stirrups must be well anchored

Instructor:

Eng. Mazen Alshorafa

Design of Concrete Structure I

University of Palestine

Page 16

Shear and Diagonal Tension in Beam

Critical Section for Shear

Instructor:

Eng. Mazen Alshorafa

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