BRAE433 Lecture Ch 4

BRAE433 Lecture Ch 4 - RC Design Ch 4 Shear in Beams BRAE...

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1 RC Design BRAE Cal Poly Ch 4 – Shear in Beams Introduction - Shear Shear (like bending moments) create tensile stresses Concrete is not good in tension BRAE Cal Poly
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2 Introduction - Shear Bending stress and Shear stress BRAE Cal Poly BRAE Cal Poly
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3 Bending Stresses • Flexure Formula (from Ch 1) –f b = Mc/I or M/S x where S x = I/c b = calculated bending stress, psi – M = applied moment – c = distance from the neutral axis to the outside BRAE Cal Poly tension or compression fibre of the beam – I = moment of inertia of the cross section about the neutral axis (Rect Beam I = bh 3 /12) unit vertical shear ν Shear Stresses unit vertical shear - ν = V x Q / (I x b) = Vh 2 / (8 I) where, V = external shear Q = static moment of area about NA I = moment of inertia of the cross section about the NA BRAE Cal Poly I = moment of inertia of the cross section about the NA b = width of the cross section ν = V x Q / (I x b) = Vh 2 / (8 I) rectangular beam
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4 Isolation of a small element f b = 0 BRAE Cal Poly Horizontal shear stresses (v) are equal in magnitude to the vertical shear stresses BRAE Cal Poly Courtesy: Mr. Hopkins
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5 Shear stresses on inclined plane 0.707 ν 0.707 ν 1.414 ν ν BRAE Cal Poly Plane at 45 Deg angle subject to tension and if the “diagonal tension” is large enough, must be reinforced Shear reinforcement Shear Span Cracks… vertical stirrups Stirrups - protect ½ way to neighbor BRAE Cal Poly inclined stirrups main reinforcement bent up at ends
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6 Concrete only - Shear V c V c = 2 x (f' c ) 0.5 x b w x d (concrete shear strength) Vu ( from factored loads ) must be less than or equal ½ x φ V c (
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This note was uploaded on 01/13/2011 for the course BRAE 433 taught by Professor Styles during the Fall '10 term at Cal Poly.

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BRAE433 Lecture Ch 4 - RC Design Ch 4 Shear in Beams BRAE...

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