![]() Determine the tension in the cable and the reaction at each pair of wheels. The cart is held in position by the cable. The gross weight of the car and its load is 5500 lb, and it is applied at at G. A loading car is at rest on an inclined track. Determine the cable tension by solving the equation for the sum of force components parallel to the track. Determine the reactions at the wheels by solving equations for the sum of moments about points above each axle. Check the values obtained.Ĭreate a free-body diagram for the car with the coordinate system aligned with the track. Determine the reactions at A by solving the equations for the sum of all horizontal forces and all vertical forces. Check the values obtained for the reactions by verifying that the sum of the moments about B of all forces is zero.ġ0 Sample Problem 4.1 Determine B by solving the equation for the sum of the moments of all forces about A. Determine the components of the reactions at A and B. The center of gravity of the crane is located at G. It is held in place by a pin at A and a rocker at B. A fixed crane has a mass of 1000 kg and is used to lift a 2400 kg crate. Determine the reactions at A by solving the equations for the sum of all horizontal force components and all vertical force components. Note there will be no contribution from the unknown reactions at A. More unknowns than equations Fewer unknowns than equations, partially constrained Equal number unknowns and equations but improperly constrainedĩ Sample Problem 4.1 SOLUTION: Create a free-body diagram for the crane.ĭetermine B by solving the equation for the sum of the moments of all forces about A. The 3 equations can not be augmented with additional equations, but they can be replaced The 3 equations can be solved for no more than 3 unknowns. Reactions equivalent to a force of unknown direction and magnitude and a couple.of unknown magnitudeħ Equilibrium of a Rigid Body in Two Dimensionsįor all forces and moments acting on a two-dimensional structure, Equations of equilibrium become where A is any point in the plane of the structure. ![]() Reactions equivalent to a force of unknown direction and magnitude. ![]() Reactions equivalent to a force with known line of action.Ħ Reactions at Supports and Connections for a Two-Dimensional Structure Include the dimensions necessary to compute the moments of the forces.ĥ Reactions at Supports and Connections for a Two-Dimensional Structure These usually consist of reactions through which the ground and other bodies oppose the possible motion of the rigid body. Indicate point of application and assumed direction of unknown applied forces. Indicate point of application, magnitude, and direction of external forces, including the rigid body weight. Select the extent of the free-body and detach it from the ground and all other bodies. ![]() The necessary and sufficient condition for the static equilibrium of a body are that the resultant force and couple from all external forces form a system equivalent to zero, Resolving each force and moment into its rectangular components leads to 6 scalar equations which also express the conditions for static equilibrium,Ĥ Free-Body Diagram First step in the static equilibrium analysis of a rigid body is identification of all forces acting on the body with a free-body diagram. Reactions at Supports and Connections for a Two-Dimensional Structure Equilibrium of a Rigid Body in Two Dimensions Statically Indeterminate Reactions Sample Problem 4.1 Sample Problem 4.3 Sample Problem 4.4 Equilibrium of a Two-Force Body Equilibrium of a Three-Force Body Sample Problem 4.6 Equilibrium of a Rigid Body in Three Dimensions Reactions at Supports and Connections for a Three-Dimensional Structure Sample Problem 4.8ģ Introduction For a rigid body in static equilibrium, the external forces and moments are balanced and will impart no translational or rotational motion to the body. 2 Contents Introduction Free-Body Diagram
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