Chapter 5

2. Design of Concrete Structure I University of Palestine بسم الله الرحمن الرحيم Chapter 5 Instructor: Eng. Mazen Alshorafa

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. Design of Concrete Structure I University of Palestine Page 8 Shear and Diagonal Tension in Beam Cracks in Beams Instructor: Eng. Mazen Alshorafa

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. Design of Concrete Structure I University of Palestine Page 16 Shear and Diagonal Tension in Beam Critical Section for Shear Instructor: Eng. Mazen Alshorafa