Prof.Kodali Srinivas

  couple of Forces A couple is defined as two parallel forces with the same magnitude    but opposite in direction separated by a perpendicular distance d. The net external effect of a couple is that the net force equals zero and the magnitude of the net moment equals = F.d  The resultant of a couple at any point is always a pure constant moment  and equal to        M = F d Problem : 2.7 A 6 m-long simply supported beam carries a anti clockwise couple 400 N-m and a point load as shown in Fig. Calculate support reactions Solution: Let the vertical reaction at support A is Ra and at support B is Rb . Here the vertical forces are upwards reactive forces Ra ,Rb and downward point load of 1000 N. The horizontal pair of forces are formed as a couple and its resultant is a moment of 400N-m Apply the  equilibrium equation is: ∑ Fy = 0 R a  + R b  - 1000 = 0       R a  + R b    = 1000...

If the beams are subjected to distributed loads like uniformly distributed load ( U.D.L. ) or distributed uniformly varying load ( U.V.L. ),in the analysis we can replace these loads by an equivalent load.  The magnitude of net equivalent point load is equal to total distributed load and acts at the centroid of the loading diagram. When solving for reactions, the following steps are recommended: Draw the beam free body diagram with support reactions and loads. Replace the uniform distributed load (if any) with the equivalent point load. If the loading (UDL) diagram is rectangle, the equivalent point load is W = wL, and its point of application is L/2 (mid point of the figure) If the loading (UVL) diagram is triangle, the equivalent point load is W = wL/2, and its point of application is L/3 as shown in the figure Solve ΣFx = 0 (sum of all horizontal forces) for finding the horizontal reaction (if any)  Solve ΣM A = 0 (sum of moments about support A) or  Solve ΣM B ...

Problem : 2.1 Determine the support reactions of a simply supported beam, with a point load W, at a point as shown in fig.  Solution :   Assigning the unknown support reactions     R A   and R B  at supports as shown in the figure. Applying the three equilibrium equations to find the three unknowns in this way: Along direction x, there is no imposed force applied to the structure.  Thus the first equilibrium equation is: ∑ Fx = 0 Unless there is an imposed load along the beam longitudinal x - axis, this reaction will always be zero. Along direction y, the imposed force P is applied to the center of the beam, as well as support reactions.   Thus the second equilibrium equation is: ∑ Fy = 0 R A + R B - W = 0         -----(1) For the third equation ∑ Mxy = 0 we have to choose one point around which the moments are calculated. It is often more...

The Support Reactions in Beams depends on the type of support on which the beam is supported. Types of supports There are 3 types of supports 1. Roller support:   If a beam is supported on a roller support then it can't in vertical direction but it can move in horizontal direction and can have rotational motion about that support. Hence total support reactions are 1 i.e in vertical direction. 2. Hinge support / Pinned support   Similarly hinge support restricts vertical and horizontal motion but beam is free to perform rotational motion. Hence it has 2 support reactions i.e horizontal and vertical 3. Fixed / Build in support:   Here the support restricts all kinds of motion. The can't perform horizontal, vertical and rotational motion. Hence it has 3 support reactions i.e horizontal, vertical and rotational reactions. Types of Beams A beam is a structural member designed to support various loading applied at points along the member.  The forces / loads applied to a b...