Horizontal Shear Stress in Beam Lecture Number 05

Horizontal Shear Stress in Beam Lecture Number - 05 D. B. Raut Mechanical Engineering SINHGAD COLLEGE OF ENGG , Vadgaon Strength of Materials

Average Shear Stresses in Beam • Average vertical shear stress in beam is defined as • Vertical shear force can be determined from shear force diagram • The shear force is purely function of the loading only. i. e. It does not depend on material properties and section of the beam • Thus average shear stress depends on loading and sectional area of the beam Strength of Materials

Maximum Shear Stress in Beam: Rectangular Section • Shear stress at a distance y from neutral axis is given by • Substituting following values in above equation Strength of Materials

Maximum Shear Stress in Beam: Rectangular Section • Simplified expression for shear stress is • Hence for maximum shear stress in rectangular beam is 1. 5 times average shear stress and it occurs at neutral axis Strength of Materials

Shear Stresses in Beam • For circular cross section Strength of Materials

Shear stress in beam: Numerical • Q. A beam AB of span 3 m and width 90 mm is loaded as shown in the diagram. Knowing σall=12 MPa, and τall=0. 8 Mpa, determine minimum depth ‘d’ of the beam • SFD and BMD are shown in the diagram • Maximum Shear force and Bending Moment are- Strength of Materials

Strength of Materials

Shear stress in beam: Numerical • Design based on allowable Normal Stress Strength of Materials

Shear stress in beam: Numerical • Design based on allowable Shear Stress • Thus in order to keep shear as well as normal stresses within allowable limits minimum depth of the beam must be 322 mm Strength of Materials