Shear Stress in Beams Figure: 07-00CO

Shear in Straight Members Internal shear force – creates shear deformation, strain and shear stress! Figure: 07-01 Note: due to nature of shear stress get transverse and longitudinal strain.

Physical example – when boards glued together, shear stress is developed at surfaces which prevents slippage. Figure: 07-02a

Notice deformation: key point, deformation not uniform!! Figure: 07-03a,b

6.2 – Shear Stress Formula: Figure: 07-04a

Derivation of Beam Shear Stress Equation: Figure: 07-04-02d

Derivation of Beam Shear Stress Equation (cont’d): Recall, dM/dx = V = Q Internal Shear (lb) Figure: 07-04-02d First Moment of area (in3) at point of interest Thickness of cross-section at point of interest (in) Moment of inertia of entire cross section (in4)

Example: Square Cross-section: Figure: 07-04-03UN

Example: I-Beam Figure: 07-07a

7-11: Given: A cantilever beam with 35 Kip load at the end 7-11: Given: A cantilever beam with 35 Kip load at the end. Sketch the intensity of the shear-stress distribution acting over the beam’s cross-sectional area and determine the resultant shear force acting on the segment AB. Question: where would you expect max stress to be? Why would you be interested in shear stress at joint? Figure: 07-12-05P7.11