Transcription of DESIGN FOR SHEAR2008
1 Dr. Mohammed E. Haque, PE. Shear DESIGN Page 1 of 6. DESIGN FOR SHEAR. Max. Shear due to loads, Vu DESIGN Shear Capacity, Vn Where = DESIGN Shear Capacity, Vn = [ DESIGN Shear strength of concrete, Vc + DESIGN Shear strength of reinforcement, Vs ]. Vn = Vc + Vs Therefore, Vu [ Vc + Vs ]. Shear force that concrete can resist without web reinforcement , Vc (ACI Eq. ) Vc = 2 fc' (bw x d ). where fc' is in psi; bw and d are in inches 1 Vu bw 45 0 d 1 section 1-1. d Fig. 1. Dr. Mohammed E. Haque, PE. Shear DESIGN Page 2 of 6. d s Number of stirrups crossing the crack, n=d/s Vu 45 0.
2 Fig. 2. Vs = Av x fy x n Vs = Av x fy x d/s (ACI ). s = Av x fy x d / Vs where Av = cross -sectional area of each stirrup has crossed the crack Av = 2 times the cross -sectional area of the stirrup bar. Av = 3 times the cross -sectional area of the stirrup bar. Fig. 3. Dr. Mohammed E. Haque, PE. Shear DESIGN Page 3 of 6. Fig. 4 Flow Chart Vertical Shear Reinforcement DESIGN (Dr. Mohammed E. Haque, ). Known: fc', fy, d, bw and Vu = = 1 for normal weight concrete; for Vc = 2 fc'. bw d sand-lightweight concrete; for all lightweight concrete Vs = [Vu - Vc] Yes section should be 8 fc'.
3 Bw d < [ Vs ] enlarged. No No No shear Determine spacing of reinforcement is vertical U stirrups based Vu > Vc on minimum shear necessary reinforcement Determine Yes required spacing of vertical U. stirrups based on No Yes Vs Vu > Vc S is smaller of the two: S = Av fy d /[Vu - Vc]. S = Av fy /[50 bw] S must be S = Av fy /[ fc' . bw] S d/2 24 in S must be If [Vu - Vc] > 4 fc'. bw d S d/2 24 in S d/4. draw the beam and show reinforcement and spacing Dr. Mohammed E. Haque, PE. Shear DESIGN Page 4 of 6. A. d Support A. width = w1 d section A-A. bw of Symmetry wu A B.
4 L. RA = wu x L /2 RB = wu x L /2. d + w1. RA. Vu at Critical section Shear carried by Vu - Vc stirrups Vs Vu Shear carried by concrete Vc Vc Vc Minimum Shear reinforcement Shear reinforcement required Shear reinforcement not required Fig. 5 Shear Reinforcement requirements Dr. Mohammed E. Haque, PE. Shear DESIGN Page 5 of 6. Summary (Vertical Stirrup or Web Reinforcement DESIGN ). 1. draw Shear, Vu Diagram (Fig. 5). 2. Calculate Vu at a distance d from the face of support 3. On the Vu diagram, identify locations where (1) Shear Reinforcement required, (2) where shear reinforcement not required, (3) where shear carried by stirrups, Vs , and (4) where minimum shear reinforcement required (Shear carried by concrete, Vc ).
5 [Note: SEE Fig. 5]. 4. Calculate Vc = 2 fc' (bw x d), where = ;. = 1 for normal weight concrete; for sand-lightweight concrete; for all lightweight concrete. 5. Calculate Vs = [Vu - Vc]. Check: If 8 fc'. bw d < [ Vs ], then section SHOULD BE ENLARGED [STOP AT THIS STEP]. 6. No Stirrups are needed if Vu < Vc DESIGN STIRRUPS. 7. Determine required spacing of vertical U stirrups based on Vs Calculate theoretical stirrup spacing, S = Av x fy x d / [Vu - Vc]. S must satisfy S d/2 24 inch If [Vu - Vc] > 4 fc'. bw d Then S d/4. Dr. Mohammed E. Haque, PE. Shear DESIGN Page 6 of 6.
6 8. Determine spacing of vertical U stirrups based on minimum shear reinforcement. S is smaller of the two: S = Av fy /[50 bw]. S = Av fy /[ fc' . bw]. S must satisfy S d/2 24 inch 9. Minimum practical stirrup spacing is 3 to 4 inches. 10. draw the beam and show the shear reinforcements and spacing.
