Prof.Kodali Srinivas

The  M oment Distribution method   is a  structural analysis  method for  statically indeterminate   beams  and  frames  developed by  Hardy Cross ,   in 1930 . The moment distribution method falls into the category of   displacement method   of structural analysis. The method only accounts for flexural effects and ignores axial and shear effects. In the moment distribution method, every joint of the structure to be analysed is fixed so as to develop the  fixed-end moments . Then each fixed joint is sequentially released and the fixed-end moments (which by the time of release are not in equilibrium) are distributed to adjacent members until equilibrium is achieved.  The moment distribution method in mathematical terms can be demonstrated as the process of solving a set of simultaneous equations by means of iteration. Distribution factors When a joint is released and begins to rotate under the unbalanced moment, resisting forces develop at each member framed together at the joint. Altho

A beam with both ends fixed is called as Fixed Beam. Fixed beams are statically indeterminate to the 2 nd  degree, and any structural analysis method applicable on  statically indeterminate  beams can be used to calculate the fixed end moments.   The  moment distribution method ,  slope deflection method  and the  matrix method  make use of the fixed end moments. Fixed End Moments in standard loading 

Example : 1 Analyse the statically indeterminate beam shown in the figure Members AB, BC, CD have the same length  . Flexural rigidities are EI, 2EI, EI respectively. Concentrated load of magnitude   acts at a distance   from the support A. Uniform load of intensity   acts on BC. Member CD is loaded at its midspan with a concentrated load of magnitude  . Note: In the following calcuations, clockwise moments and rotations are positive. Fixed end moments Slope deflection equations Joint equilibrium equations Joints A, B, C should suffice the equilibrium condition. Therefore Rotation angles The rotation angles are calculated from simultaneous equations above. Member end moments Substitution of these values back into the slope deflection equations yields  the member end moments (in kNm):

ASSIGNMENT NO : 1 1. a) Explain in briefly the different types of failures of riveted joints with suitable          sketches.     b) A double riveted double cover butt joint is used to connect plates 12mm thick.           Determine the diameters of the rivet, rivet value,pitch and efficiency of the joint.          Adopt the permissible stress in plate for axial tension  may be taken as 0.6 f y ,           f y =250N/mm 2 and power driven shop rivets. 2. a) State the assumptions in the theory of riveted joints.     b) The truss members meeting at  a bottom joint as shown           in figure. Design the riveted Joint connection by 10mm           thick gusset plate. Sketch also the joint details.Using the           Power driven field rivets. 3. a) What are the advantages of welded joints over riveted joints?     b) Design a suitable longitudinal fillet weld to connect 150x8mm plate to 150x10mm          Plate to transmit a pull, equal strength of small plate. Assume welding is to be ma

June-2010 Click on Fig to Get Large  Image.  June-2010 June-2010 Click on Fig to Get Large  Image.    December -2010 Decenber -2010

Direct Central Impact A collision is an isolated event in which two or more moving bodies (colliding bodies) exert forces on each other for a relatively short time. A high force applied over a short time period when two or more bodies collide is called as Impact. Types of Impact 1.Elastic Impact 2.Plastic Impact or Inelastic Impact If the two objects adhere and remain connected after the impact, the impact is said to be perfectly plastic. Coefficient of Restitution During the impact, each object can lose energy This loss in energy can be expressed as the difference in velocity after the collision divided by the difference in velocity before the collision, or The prime velocities, v B '  and v A '  are velocities after the collision. The coefficient of restitution is a measure of the energy that is lost during a collision.  For a perfectly elastic collision (e = 1), no energy is lost. The Coefficient of Restitution for small rubber balls is very c

  Impulse and  Momentum     In classical mechanics, an  impulse  is defined as the integral of a force with respect to time. When a force is applied to a rigid body it changes the momentum of that body. A small force applied for a long time can produce the same momentum change as a large force applied briefly, because it is the product of the force and the time for which it is applied that is important.  The impulse is equal to the change of momentum. If both sides of the above equation are multiplied by the quantity t, a new equation results. The quantity(Force X time) is known as  impulse .  Impulse  I  produced from time  t 1  to  t 2  is defined to be where  F  is the force applied from  t 1  to  t 2 . Momentum can be defined as "mass in motion."  In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object. Momentum = mass x velocity    = m x v