Published on December 27, 2013
Presented by Md. Shariful Islam Student ID: 10.01.03.112 Department of Civil Engineering AUST, Dhaka
Course Teachers Lecturer Mr. Galib Muktadir Ratul Lecturer Ms. Sabreena Nasrin Department of Civil Engineering Ahsanullah University of science and Technology
EQUILIBRIUM OF NON-CONCURRENT COPLANAR FORCE SYSTEM When a body is in equilibrium, it has neither translatory nor rotatory motion in any direction. Thus the resultant force R and the resultant couple M are both zero, and we have the equilibrium equations for two dimensional force system Fx = 0; Fy = 0 M=0 These requirements are both necessary and sufficient conditions for equilibrium.
Supports: A structure is subjected to external forces and transfers these forces through the supports on to the foundation. Therefore the support reactions and the external forces together keep the structure in equilibrium. Types of supports There are different types of supports. Some of them are a) Roller Support b) Hinged or pinned support c) Fixed or built in support Some supports are shown in the figure along with the reactions that can be mobilised.
Real example of various supports systems Roller Support
Action on body Types of Supports (a) Flexible cable ,belt ,chain, rope BODY BODY T Force exerted by cable is always a tension away from the body in the direction of cable Contact forces are normal to the surfaces (b) Smooth surfaces F F
(c) Roller support Contact force is normal to the surface on which the roller moves. The reaction will always be perpendicular to the plane of the roller . Roller support will offer only one independent reaction component.(Whose direction is known.)
( d )pinned Support / hinged support Rh θ R Rv This support does not allow any translatory movement of the rigid body. There will be two independent reaction components at the support. The resultant reaction can be resolved into two mutually perpendicular components. Or it can be shown as resultant reaction inclined at an angle with respect to a reference direction.
(e) Fixed or Built-in Support M RH Rv M This type of support not only prevents the translatory movement of the rigid body, but also the rotation of the rigid body. Hence there will be 3 independent reaction components of forces. Hence there will be 3 unknown components of forces, two mutually perpendicular reactive force component and a reactive moment as shown in the figure.