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MAE 241 - Statics

Summer 2009

Dr. Konstantinos A. SierrosOffice Hours: M and W 10:30 11:30 (263 ESB new add)

kostas.sierros@mail.wvu.eduTeaching Blog: http://wvumechanicsonline.blogspot.com

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The frictional effects of the air on the blades of the standing fan create acouple moment of on M o = 6 Nm on the blades. Determine the magnitudeof the couple forces at the base of the fan so that the resultant couple

moment on the fan is zero.

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Replace the force system acting on the beam by an equivalent force andcouple moment at point B.

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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 thesignificance of each force acting on the diagram.

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Draw the free-body diagram of the beam which supports the 80-kg loadand 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.

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5.4 Two and three force members

Two force membersA two force member has forces applied at only two

points on the member To satisfy equilibrium F A and F B must be

equal in magnitude but opposite in directionTherefore, for two force members to be in equilibriumThe forces must have the same magnitude, oppositedirections and have the same line of action, directedalong the line joining the two points where these forcesact

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5.4 Two and three force members

Three force membersA three force member has forces applied atonly three points on the member Moment equilibrium can be satisfied only

if three forces form a cocurrent or parallel

force system

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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

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5.6 Equations of equilibrium

Vector equations of equilibriumF = 0 and M = 0

Scalar equations of equilibriumF x = 0 and M x = 0F y = 0 and M y = 0F

z= 0 and M

z= 0

At most six unknowns

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5.7 Constraints and statical determinacy

Redundant constraints Redundant supports are necessary to holdthe body in equilibrium Statically indeterminate problems are theones where there are more unknown

loadings on the body than availableequations of equilibrium

Unknown loadings : M A, A x, A y, B y, C y

Equilibrium equations available:F x = 0, F y = 0, M o = 0

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5.7 Constraints and statical determinacy

Improper constraintsHaving the same number of unknown reactive forces as availableequations of equilibrium does not always guarantee that a body will bestable when subjected to a particular loading

Applied loading P will cause the beam to rotate slightly about A, so the beam is improperly constrained, M A0