Mae 241-lec8
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MAE 241 - Statics Summer 2009
Dr. Konstantinos A. Sierros Office Hours: M and W 10:30 – 11:30 (263 ESB new add) [email protected] Teaching Blog: http://wvumechanicsonline.blogspot.com
The frictional effects of the air on the blades of the standing fan create a couple moment of on Mo = 6 Nm on the blades. Determine the magnitude of the couple forces at the base of the fan so that the resultant couple moment on the fan is zero.
Replace the force system acting on the beam by an equivalent force and couple moment at point B.
Draw the free-body diagram of the 50-kg paper roll which has a center of mass at G and rests on the smooth blade of the paper hauler. Explain the significance of each force acting on the diagram.
Draw the free-body diagram of the beam which supports the 80-kg load and is supported by the pin at A and a cable which wraps around the pulley at D. Explain the significance of each force on the diagram.
5.4 Two and three force members Two force members A two force member has forces applied at only two points on the member • To satisfy equilibrium FA and FB must be equal in magnitude but opposite in direction Therefore, for two force members to be in equilibrium The forces must have the same magnitude, opposite directions and have the same line of action, directed along the line joining the two points where these forces act
5.4 Two and three force members Three force members A three force member has forces applied at only three points on the member • Moment equilibrium can be satisfied only if three forces form a cocurrent or parallel force system
5.5 Equilibrium in 3D – Free-body diagrams Support reactions • A force is developed by a support that restricts the translation of its attached member • A couple moment is developed when rotation of the attached member is prevented
5.6 Equations of equilibrium
Vector equations of equilibrium ΣF = 0 and ΣM = 0
Scalar equations of equilibrium ΣFx = 0 and ΣMx = 0 ΣFy = 0 and ΣMy = 0 ΣFz = 0 and ΣMz = 0 At most six unknowns
5.7 Constraints and statical determinacy Redundant constraints • Redundant supports are necessary to hold the body in equilibrium • Statically indeterminate problems are the ones where there are more unknown loadings on the body than available equations of equilibrium Unknown loadings : MA, Ax, Ay, By, Cy Equilibrium equations available: ΣFx = 0, ΣFy = 0, ΣMo = 0
5.7 Constraints and statical determinacy Improper constraints Having the same number of unknown reactive forces as available equations of equilibrium does not always guarantee that a body will be stable when subjected to a particular loading
Applied loading P will cause the beam to rotate slightly about A, so the beam is improperly constrained, ΣMA≠0
Dr. Konstantinos A. Sierros Office Hours: M and W 10:30 – 11:30 (263 ESB new add) [email protected] Teaching Blog: http://wvumechanicsonline.blogspot.com
The frictional effects of the air on the blades of the standing fan create a couple moment of on Mo = 6 Nm on the blades. Determine the magnitude of the couple forces at the base of the fan so that the resultant couple moment on the fan is zero.
Replace the force system acting on the beam by an equivalent force and couple moment at point B.
Draw the free-body diagram of the 50-kg paper roll which has a center of mass at G and rests on the smooth blade of the paper hauler. Explain the significance of each force acting on the diagram.
Draw the free-body diagram of the beam which supports the 80-kg load and is supported by the pin at A and a cable which wraps around the pulley at D. Explain the significance of each force on the diagram.
5.4 Two and three force members Two force members A two force member has forces applied at only two points on the member • To satisfy equilibrium FA and FB must be equal in magnitude but opposite in direction Therefore, for two force members to be in equilibrium The forces must have the same magnitude, opposite directions and have the same line of action, directed along the line joining the two points where these forces act
5.4 Two and three force members Three force members A three force member has forces applied at only three points on the member • Moment equilibrium can be satisfied only if three forces form a cocurrent or parallel force system
5.5 Equilibrium in 3D – Free-body diagrams Support reactions • A force is developed by a support that restricts the translation of its attached member • A couple moment is developed when rotation of the attached member is prevented
5.6 Equations of equilibrium
Vector equations of equilibrium ΣF = 0 and ΣM = 0
Scalar equations of equilibrium ΣFx = 0 and ΣMx = 0 ΣFy = 0 and ΣMy = 0 ΣFz = 0 and ΣMz = 0 At most six unknowns
5.7 Constraints and statical determinacy Redundant constraints • Redundant supports are necessary to hold the body in equilibrium • Statically indeterminate problems are the ones where there are more unknown loadings on the body than available equations of equilibrium Unknown loadings : MA, Ax, Ay, By, Cy Equilibrium equations available: ΣFx = 0, ΣFy = 0, ΣMo = 0
5.7 Constraints and statical determinacy Improper constraints Having the same number of unknown reactive forces as available equations of equilibrium does not always guarantee that a body will be stable when subjected to a particular loading
Applied loading P will cause the beam to rotate slightly about A, so the beam is improperly constrained, ΣMA≠0
