Prof.Kodali Srinivas

Short Answer Questions: 1.What do you mean by direct stress and bending stress?  2 Draw stress distribution across the section due to Bi axial bending stress and direct stress.  3 Find core diameter of a solid circular section, if diameter is ‘d’  4 Explain about the term kernel and determine the size of kernel for a rectangular section 200 mm x 300mm  5 Explain the conditions for stability of dam.  6 Find core diameter of a hollow section, if external and internal diameter are ‘D’ and ‘d’. Assignment : 1 A hollow rectangular column of external depth of 1 m and external width 1 m is 10 cm thick.. Calculate the maximum and minimum stress in the section of the column, if vertical load of 200 kN is acting with an eccentricity of 20 cm. 2 A short column of external diameter 40 cm and internal diameter 20 cm carries an eccentric load of 80 kN. Find the greatest eccentricity which the load can have without producing tension on the cr...

 Assignment : 1. the stresses and deflection for the mid section of the I beam by unsymmetrical method Also identify the position of the neutral axis  2. A 240 mm × 120 mm steel beam of I-section is simply supported over a span of 6m and carries two equal concentrated loads at points 2 m from each end. The properties of the section are Ixx = 6012.32 × 104mm4, Iyy = 452.48 × 104 mm4. a) Determine the magnitude of the loads when the plane of the loads is vertical through YY. The permissible stress is 150 N/mm2 in compression and tension. b) Determine the degree of inclination of the plane of these loads to the vertical principal plane YY that will result in 20 percent greater bending stress than permitted under (A)  3. A T-Section of dimensions 150 wide x 200 mm deep, with 10 mm thickness of flange and web, is used as simply supported a beam on a span of 6 m. Find the maximum value of ‘w’ in kN/m, the permissible stress in the material is 120 MPa. The plane of loading is in...

When the plane of bending does not coincide or parallel to the plane containing the principal centroidal axis of cross section is called as unsymmetrical bending. It is also known as complex or bi axial bending. When a section of a beam is not symmetrical about the plane of bending, or the applied load is not coincide with the plane of bending an unsymmetrical bending takes place, i.e., in addition to bending, due to applied loads twisting is observed in the beam. In unsymmetrical bending, the direction of the neutral axis will not be perpendicular to the plane of bending. To prevent the torsion, the line of application of the load must pass through the shear center. If it does not, the beam undergoes the combined bending and torsion loading. Analysis of unsymmetrical bending If the plane of the bending moment is perpendicular to the neutral surface, we may use simple bending equation. This condition will occurs only if the bending axes X and Y axes are p...

For analyzing the stresses in unsymmetrical bending of the beam section we required principal Moment of Inertia about bending axis. The product of inertia is used for calculating Principal Moment of Inerti a. 1. Product of Inertia The product of inertia of an area A relative to the indicated XY rectangular axes is I XY = ∫ xy dA The value of product of inertia depends on the position and orientation of selected axes 1. The value of the product of inertia may be positive negative or zero. 2. If the total area lies in the first and third quadrant it will be positive. If the total area lies in a second and fourth quadrant it will be negative. 3. If there has one axis of symmetry the product of inertia will be zero, because the left part of the axis is canceled the right part. Parallel axis theorem for products of inertia: The product of inertia with respect to any pair of the axis in its plane is equal to the product of inertia with respect to the parallel centroidal a...

The Area Moment Of Inertia or Second Moment of Area is a geometrical property of a beam and depends on a reference axis.  The Moment of Inertia of a beam's cross-sectional area measures the beams ability to resist bending. The larger the Moment of Inertia the less the beam will bend.  The smallest Moment of Inertia about any axis passes through the centroid. The following are the mathematical equations to calculate the Moment of Inertia: I x equ. (1) I y equ. (2) Where , y is the distance from the x axis to an infinitesimal  area dA. x is the distance from the y axis to an infinitesimal  area dA. Perpendicular  axis theorem  The moment of inertia of a plane area about an axis normal to the plane is equal to the sum of the moments of inertia about any two mutually perpendicular axes lying in the plane and passing through the given axis. I zz = I xx + I yy Polar Moment of Inertia The Moment Of Inertia of an area about an axis perpendicular to...