# HIghtlights

1.           The principle of equilibrium states that a stationary body will be in equilibrium if the algebraic sum of all the forces is zero and also the algebraic sum of moments of all the external forces is zero.
2.           The conditions of equilibrium are written mathematically as ƩFx = 0, ƩFy = 0, and ƩM = 0. The sign Ʃ is known as sigma and this sign represents the algebraic sum.
3.           When a body is subjected to two forces, the body will be in equilibrium if the two forces are collinear, equal and opposite.
4.           Two equal and opposite parallel forces produces a couple whose moment is equal to either force multiplied by their perpendicular distance.
5.           If three concurrent forces are acting on a body and the body is in equilibrium, then the resultant of two forces should be equal and opposite to the third force.
6.           Free body diagram of a body is a diagram in which the body is completely isolated from its support and the supports are replaced by the reactions which these supports exert on the body.
7.           The reaction at the knife edge support will be normal to the surface of the beam.
8.           The reaction in case of roller support will be normal to the surface of roller base.
9.           The reaction at the hinged end (or pinned end) will be either vertical or inclined depending upon the type of loading. If the load is vertical, then reaction will be vertical. But if the load is inclined, then the reaction will also be inclined.
10.        For a smooth surface, the reaction is always normal to the support.
11.        A load, acting at a point on a beam, is known as point load or concentrated load.
12.        If each unit length of the beam carries same intensity of load, then that type of load is known as uniformly distributed load which is written as U.D.L.
13.        The reactions of a beam can be determined by analytical method and graphical method.
14.        The reactions by analytical method are obtained by using equations of equilibrium, i.e., ƩFx = 0, ƩFy = 0, and ƩM = 0.
15.        The reactions by graphical method are obtained by drawing a space diagram and a vector diagram.
16.        If a beam is loaded with inclined loads, then the inclined loads are resolved normal to the beam and along the beam. Now the equiation of equilibrium are used for finding reactions.
17.        The reaction on roller support is at right angles to the roller base.
18.        The forces in the members of a frame are determined by :
(i)Method of joints
(ii)Method of sections, and
(iii)Graphical method.
19.        The force in a member will be compressive if the member pushes the joint to which it is connected whereas the force in the member will be tensile if the member pulls the joint to which it is connected.
20.        While determining forces in a member by method of joints, the joint should be selected in such a way that at any time there are only two members, in which the forces are unknown.
21.        If three forces act at a joint and two of them are along the same straight line then third force would be zero.
22.        If a truss (or frame) carries horizontal loads, then the support reaction at the hinged end will consists of (i) horizontal reaction and (ii) vertical reaction.
23.        If a truss carries inclined loads, then the support reaction at the hinged end will consists of: horizontal reaction and (ii) vertical reaction. They will be given as :
Horizontal reaction = Horizontal components of inclined loads
Vertical reaction = Total vertical components of inclined loads – Roller support reaction
24.        Method of section is mostly used, when the forces in a few members of a truss are to be determined.
25.        The following steps are necessary for obtaining a graphical solution of a frame:
(i)               Making a space diagram,
(ii)            Constructing a vector diagram, and
(iii)          Preparing a force table.
26.        The various members of a frame are named according to Bow’s notation.