Chapter 7 Shear Resistance
Chapter 7 Shear Resistance
7.1 Shear Failure of RC Beams without Shear Reinforcement 7.1.1 Shear in homogeneous beams In mechanics of materials,the shear stress of homogeneous各向同性，elastic and uncracked beams can be calculated by S T二 Ib where -shear force S-first moment of area (S=4
7.1 Shear Failure of RC Beams without Shear Reinforcement 7.1.1 Shear in homogeneous beams • In mechanics of materials, the shear stress of homogeneous各向同性, elastic and uncracked beams can be calculated by VS I b τ where V - shear force S – first moment of area ( S A y )
Load My S O= t= I Ib 回萨， , +x2 2 4 (a) Reaction (b) 2 +x2 中 白 (c) Fig.7.1-1 Normal,shear and principal stresses in homogeneous uncracked beam.(a)Flexural and shear stresses acting on elements in shear span;(b)distribution of shear stress;(c) principal stresses on elements in shear span
(a) (b) (c) Fig. 7.1-1 Normal, shear and principal stresses in homogeneous uncracked beam. (a) Flexural and shear stresses acting on elements in shear span; (b) distribution of shear stress; (c) principal stresses on elements in shear span I My 2 2 1 2 4 2 2 2 2 4 - ) 2 arctan( 2 1 - VS I b τ
Crack ys flexural and shear stresses for a RC beam neutral axis (a (b) (c) 45°<0<90° 5 (d) (e) (D Fig.7.1-3 Orientation of principal stresses.(a)Geometry and loading;(b)axial stress at section x-x;(c)shear stress distribution at section x-x;(d)segment 4;(e)segment B;(f) segment C;(g)principal compressive stress paths
• Crack vs flexural and shear stresses for a RC beam Fig. 7.1-3 Orientation of principal stresses. (a) Geometry and loading; (b) axial stress at section x-x; (c) shear stress distribution at section x-x; (d) segment A; (e) segment B; (f) segment C; (g) principal compressive stress paths
7777777 Fig.7.1-2 Principal compressive stress trajectories in an uncracked beam
Fig. 7.1-2 Principal compressive stress trajectories in an uncracked beam