![]() ![]() Rule of thumb is to find the total number of unknowns and the number of reactions!ġ9 Problem 2 A 70 kg (W) overhead garage door consists of a uniform rectangular panel AC 2100 mm high (h), supported by the cable AE attached at the middle of the upper edge of the door and by two sets of frictionless rollers at A and B. We will try to figure out the role of every component to acquaint ourselves with the system. Even before solving the problem we will first analyse it qualitatively. or like this where A, B, C are not in a straight line We can also use equations like thisġ4 Problem 1 Determine the tension in cable ABD and reaction at support C. As we will see in the later problems that it can be greatly advantageous if sometimes x and y axes are inclined. However, there is no reason why they can’t be inclined. Note that here x and y axis are horizontal and vertical. C Should emphasize this point as much as we can. More than three equations per free body is illegal. Rombergġ2 More Examples of FBD What free body we zoom into depends on what we wish to calculate! So the desired quantity of interest should never be lost track of. Concepts will get more clear as we proceed further.ġ1 Simple examples FBD FBD Copyright, Dr. Replace kinematic constraints with corresponding reactions. Means replace supports (connections) with the corresponding reactions. ![]() Zoom in on a given component of a structure. Single most important concept in engineering mechanics. Loading had only one plane of symmetry Using symmetry and static equivalence, the problem can be converted into a 2D problem This would also give us intuition about what reactions it can provide.ħ Simple Examples Roller Support Fixed SupportĨ Using Symmetry to convert 3D problems to 2D (adapted from Box has 3-planes of symmetry. From our dealings with the external mechanical world we all have intuition about how every link or support can move. This point is very important and should be emphasized as much as possible to the students. Similarly if a support freely allows motion of particular DOF then there is no reaction from the support in that direction. If a support rigidly constrains a given degree of freedom (DOF) for a rigid body then it gives rise to a reaction corresponding to that DOF. Always note that in the case of supports displacement (rotation) and force (torque) in any given direction are complementary. There is an intricate relationship between kinematics (motion) and reactions (forces). Too few supports makes system unstable general loading Too many supports make the system over-rigid. ![]() ![]() Supports are required to maintain system in equilibrium. Structure: machine, bridge, building, car, human body Subjected to various forces: gravity, wind, man-made machine, earthquake A structure is designed to typically carry certain functions Integrity of structure is essential to carry those function Simple mechanical integrity of structures is determined by how well forces are transmitted by various components To study this is the goal of this course The structure should be globally supported to prevent it from falling over. Different component of structure talk to each other via linkages. Other wise the structure will lose its integrity. The components are the be connected by linkages. 2 Equilibrium System is in equilibrium if and only if the sum of all the forces and moment (about any point) equals zero.Īny structure is made of many components. ![]()
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