 Hello everyone, myself, Ms. Shailaja Dhavarkonda, Assistant Professor in Civil Engineering Department, Wolchen Institute of Technology, Solapur. In today's lecture, we are going to study analysis of pin-jointed plane frames. At the end of this video, the viewers will be able to define plane frame and space frame. They can classify the plane frames and explain nature of the force in the member frame. A pin-jointed frame is a structure made up of the members which are pin-connected at the ends and the joints are only the capable to taking the external loads. The examples of pin-connected frames are roof trusses. Normally, if you observe the industrial sheets below the roof covering or the AC sheets, we will observe one steel structure. It is called as roof truss and bridge trusses to support the deck slab. Pin-jointed plane frames. The frame or the members which are lying in a single plane are called as plane frames and the members which will not lie in a single plane means which will lie in a different planes that is x, y and z direction is called as space frame. If you observe the building, normal building frame, it is in only x and y direction. So, for the plane frame, building frame is the perfect example and if you observe the towers of the electrical or mobile towers, it is the perfect example for the space frame. Means in mobile tower, you can see the members are in different vertical, horizontal, inclined. So, it is the perfect example for the space frame. It is further classified as perfect frame, deficient frame and redundant frame. The perfect frame which has got sufficient number of members to resist the load without undergoing appreciable deformation in shape. It means to classify the frames we have the equation m is equal to 2j minus 3 where m is equal to number of members and j is equal to number of joint. When you will satisfy this equation, it is called as perfect frame. If you observe this figure, here number of members are 3 and number of joints are 3. If you put these values of members and joints in this equation, m is equal to 2j minus 3, you will get 3 is equal to 3. So, it is called as perfect frame. Deficient frame. A frame is said to be deficient if the number of members in the frame are less than required for perfect frame. Means if here if you observe this figure, number of members are 4 and number of joints are 4. So, if you put these values of members and joints in equation m is equal to 2j minus 3, you will get 4 is equal to 2 into 4 minus 3 means it is 5. So, here 4 is less than 5. It means the members required for the perfect frame are less. So, it is called as deficient frame. Redundant frame. A frame is said to be redundant if the number of members in it are more than required for perfect frame. If you observe this figure, here number of joints are only 6 and the number of members are 11. If you put these values in equation m is equal to 2j minus 3, you will get number of members are 11 and 2j minus 3 you will get 9. Means the number of members are more than that of required frame. So, it is called as redundant frame. So, whenever you are satisfying the equation m is equal to 2j minus 3, it is perfect frame. When the number of members are less than required for perfect frame that is 2j minus 3, it is called as deficient frame and when the number of members are more than 2j minus 3 it is called as redundant frame. Then nature of forces. Each and every member will have different nature of force. There are two nature of forces compression and tension. Here in this figure at this joint the force is acting towards the joint. So, it is called as compression force. And here at this joint the force is acting away from the joint. So, it is called as tensile force. So, there are two types of nature of forces compression and tension. Now, what are the methods to analyze the frames? That is method of joint, method of section, graphical method. From these three method of joint and method of section are the analytical methods. Method of joint. At any joint the members meeting and loads acting constitute a system of concurrent forces. It means if at a joint the number of forces are meeting and the load is acting it is called as concurrent force system. We have two equilibrium equations. When these three forces meet at a point it will have two equilibrium equations that is summation f of x and summation f of y. In method of joint after determining the reactions we have to select the joint such whereas you will get only two unknowns because we are having only two equilibrium conditions. Then using two equilibrium conditions you can analyze the joint because if you observe here at joint O one external load is acting and two unknowns are there. So, you can easily find out by using summation f of x and summation f of y. Method of section. Under the following situation the method of section is preferred. When the truss will have more span and you have to find out few member forces in that case you can go for the method of section. In method of section it is adopted when you have to find the forces in only few members. If you observe this it is huge truss. So, it is not possible to find the few member forces by method of joint because if you go for the method of joint you have to calculate one reactions and afterwards you have to analyze a single joint one by one which has huge calculations. So, instead of going for the method of joint you can go for the method of section. So, in the method of section you have to find the members where you have to calculate the forces. So, in method of section the section line should pass only through three members. When the method of joint is fails in that case we will consider the method of section and after determining the reactions you have to pass the section line from only three members. The section line should pass only three members. So, here as I shown in figure the section line should only pass through three members whenever you have to calculate the forces. Now these are the some questions given related on the video. So, you pause the video and try to answer these questions. Now these are the answers. The frame is called perfect when it satisfies the equation m is equal to 2j minus 3. The nature of force towards the joint is called as compression. The nature of force away from the joint is called as tensile force. If all the members of frame do not line a single plane are known as space frame. So, these are the references considered for the further study. Thank you.