 In today's session, we are going to discuss a problem on equilibrium for connected bodies. Myself, Bipin Patil, Assistant Professor, Department of Civil Engineering, Vulture, Institute of Technology, Swarapur. So dear friends, these are the learning outcomes for today's session. So basically we will focus on these particular two points. One is the concept of your equilibrium and how to identify, how to calculate, how to analyze the forces present in a connected body. So before that, force, what do you mean by static equilibrium? You may know if we consider the system of forces, equilibrium, so for that we need to provide such types of force which keeps the structure, system, it is in rest condition. Means any system of forces that keeps the body at a rest is said to be in equilibrium. That is, the state of the body is not affected by the action of the force systems in equilibrium. Means if I consider the system of forces, so to keep this particular body it is in a rest condition, so you may apply the forces exactly in opposite direction having some magnitude. Then and then we are going to keep this particular body, it is in a rest condition. So this is nothing but your static equilibrium is there. Means this particular equilibrium is applicable on those four systems whose resultant action is zero. Let us we discuss what do we mean by a lamesthrom, lamesthrom statement. When three forces means you consider A, B, C, P, Q, R or X, Y, Z, whatever it may be. Consider here three forces A, B, C. Acting at a point or in a equilibrium means we are considering these particular three forces are in equilibrium, a single point. Then each force, each force means A, B, C. Each proportional to the sign of the angle is proportional to the sign of the angle between the other two forces. Sign of angle X, sign of angle Y, sign of angle C. Means for example you focus on this particular schematic diagram. Consider three forces that is A, B, C. Acting on a particle or in a body making angle X, Y, Z with each other. So in the equation form it is expressed according to the statement of a lamesthrom. So A that is force A and this particular force is proportional to the sign of the angle between remaining two forces. So the force A, sign of angle between remaining two forces that is X, sign X is equal to if I consider force B, so we consider here Y that is sign of Y and force C that is sign of Z is there. So this particular three forces are proportional to each other. You consider here P force, Q force, R force, consider the angle alpha, beta, gamma and same equation you generated. So the same statement we are utilizing for solving the problems. These are the few steps to determine the forces. First step, select such a joint where one known force should be there. You select your problems such joint where one force should be known. Second one you just try to draw the pre-body diagram by considering any one joint. Any one joint you select it where one force should be known and the same joint you consider for further calculation. Next apply the equilibrium equation by considering the directions summation f of X is equal to 0, f of Y is equal to 0 and movement at any one point is equal to 0. Here you consider all right hand side forces positive sign, clockwise rotary effect positive sign, vertical upward force positive sign, exactly vice versa means downward force negative sign, left hand side forces negative sign, anti-clockwise rotary effect negative sign. And then you just try to identify the unknown forces. Let's we discuss one problem why a row picks at two points A and D fixed as shown in the figure, weight 20 kiloton and 30 kiloton are attached to at joint B and C respectively. The weight rest with portion AB means this particular AB and BC inclined at here the inclination with respect to horizontal 30 degree and 50 degree respectively. Then the tension present in a segment AB, BC and CD also find also find the inclination of the segment CD means this particular you just try to identify. So our job is very simple first you consider such joint where one force should be known now here also one force is known here also one force is known, two are unknown but here angle is also known. So let's we consider joint B first pre-body diagram for joint B. One this particular BA second one BC next one the given force that is 20 kiloton it moves in an outward direction. So you consider this particular X and Y coordinate this angle is 50 degree given this one now mentioned with respect to vertical 30 degree so this is 30 so we require this whole so how to identify it. So this angle is 30 degree so total is 180, 180 minus 30 that is remaining one. So apply the Lamis theorem for this particular joint B how to apply BA force and opposite this particular 50 degree angle sign of this particular angle. So BA sign 50 BC sign 180 minus 30 is equal to 20 this whole angle how to calculate it this is 50 so remaining one 40 this is 90 this is 31 so 20, 30 plus sign of 40 plus 90 plus 30 now how to calculate this particular unknown forces equated to the given force now you observe here this BA sign 50 BC sign 180 minus 30 though both are unknown equated to 20 sign this whole particular that your angle. So BA sign 50 is equal to 20 sign 40 plus 90 plus 30 so BA is equal to 44.80 kiloton give the equation number one similarly you equate BC sign 180 minus 30 to 20 sign 40 plus 90 plus 30 similarly you calculate the value of BC so it comes 29.20 kiloton so BA and BC how to calculate it by considering the Lamis theorem. Now let us you identify consider joint C in this particular joint C we apply the static equilibrium equations all horizontal forces now this is the incline CD incline CB incline so mention the component one is this component second one is this one here also one component second one so with respect to x axis you consider here. So for example if I consider CD all horizontal forces so here CD cos 90 degree minus theta this is unknown one minus CB now I am considering with respect to x axis 50 degree is given here 40 degrees present here so CB cos 40 this is negative sign because left hand side forces arrow is there is equal to 0 this is your equation number one similarly applies second static equilibrium equation that is summation v is equal to 0 so all vertical are pulled and one is downward CD sin 90 minus theta plus CB sin 40 minus 30 is equal to 0. So you equate this particular two equations equation 1 and 2 and try to identify the value of CD and theta so after calculation CD comes 25.12 kilotone and theta 63.43 degrees there so according to that by considering the Lamis theorem and static equilibrium equation easily we can identify the unknown forces also the angles so my dear friends you just try to pause the video try to give the answer of this particular questions answer of this particular question is this one to prepare this particular session I refer this particular references thank you.