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 3m and width 90 mm is loaded as shown in the diagram. Knowing σall=12MPa, and τall=0.8Mpa, 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