![]() Such structures are known as the statically indeterminate structures. 3), then we can not evaluate reactions with only equilibrium equations. ![]() If the number of unknown reactions is more than the number of equilibrium equations (as in the case of the beam shown in Fig. They must also satisfy equilibrium equations for any part of the structure taken as a free body. Admissible or correct solution for reaction and internal stresses must satisfy the equations of static equilibrium for the entire structure. After evaluating reactions, one could evaluate internal stress resultants in the beam. ![]() Using the above three equations we could find out the reactions at the supports in the beam shown in Fig. For such structures we could express equilibrium equations as follows: The static equilibrium condition along x -direction requires that there is no net unbalanced force acting along that direction. For planar structures, the resultant of all forces may be a force, a couple or both. Also the only external moment that could act on the structure would be the one about the z -axis. For such structures we could have forces acting only in x and y directions. Now, consider planar structures lying in xy − plane. Hence, the above two equations may also be written in three co-ordinate axes directions as follows: Also, if the resultant force vector is zero then its components in three mutually perpendicular directions also vanish. A vector in 3-dimensions can be resolved into three orthogonal directions viz., x, y and z (Cartesian) coordinate axes. The equations of equilibrium are the direct consequences of Newton’s second law of motion. Hence, the book lying on the table subjected to external force as shown in Fig. ![]() Also for a body to be in equilibrium, the vector sum of all external moments ( ) about an axis through any point within the body must also vanish. However, if the body is in the state of static equilibrium then the right hand of equation (1) must be zero. M is the total mass of the body and is the acceleration vector. Is the vector sum of all the external forces acting on the body, In a simple vector equation it may be stated as follows: Eq. When does an object move and when does it not? This question was answered by Newton when he formulated his famous second law of motion. 1 (b), then book stays in the same position, as in this case the vector sum of all the forces acting on the book is zero. However, if we apply the force perpendicular to the book as in Fig. Now, if we apply a force F 1 horizontally as shown in the Fig.1(a), then it starts moving in the direction of the force. ![]() Equations of Static Equilibrium: Consider a case where a book is lying on a frictionless table surface. ![]()
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