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ELEENTS O RCHITECTURL STRUCTURES: OR, EHVIOR, ND

1 ELEENTS O RCHITECTURL STRUCTURES: OR, EHVIOR, ND DESIGN DR. NNE NICHOLS SPRING 2014 forces have the tenency to make a boy rotate about an ais lecture five moments same translation but ifferent rotation 1 Lecture 5 S2009abn 6 a force acting at a ifferent point causes a ifferent moment: 7 8 1

2 efine by magnitue an irection units: Nm, kft irection: + cw (!) C - ccw value foun from an istance also calle lever or moment arm with same : 1 2 (bigger) 9 10 aitive with sign convention can still move the force along the line of action location of moment inepenent = = - = = = Varignon s Theorem resolve a force into components at a point an fining perpenicular istances calculate sum of moments equivalent to original moment makes life easier! geometry when component runs through point, =

opposite irection istance apart cw or ccw 1 2 oment Couples equivalent couples same magnitue an irection & may

3 of a orce moments of a force introuce in Physics as Torque cting on a Particle an use to satisfy rotational equilibrium Physics an of a orce my Physics book (right han rule): 9 10 oment Couples 2 forces same size opposite irection istance apart cw or ccw 1 2 oment Couples equivalent couples same magnitue an irection & may be ifferent 300 N 100 mm 300 N 200 N 120 N 120 N not epenant on point of application 200 N 150 mm 250 mm TOPIC

oment Couples ae just like moments cause by one force can replace two couples with a single couple oment Couples moment couples in structures 300 N 100 mm 300 N + 200 N 240 N = 240 N 200 N 150 mm 250

4 oment Couples ae just like moments cause by one force can replace two couples with a single couple oment Couples moment couples in structures 300 N 100 mm 300 N N 240 N = 240 N 200 N 150 mm 250 mm Equivalent orce Systems two forces at a point is equivalent to the resultant at a point resultant is equivalent to two components at a point resultant of equal & opposite forces at a point is zero put equal & opposite forces at a point (sum to 0) transmission of a force along action line orce-oment Systems single force causing a moment can be replace by the same force at a ifferent point by proviing the moment that force cause - moments are shown as arche arrows

5 orce-oment Systems a force-moment pair can be replace by a force at another point causing the original moment Parallel orce Systems forces are in the same irection can fin resultant force nee to fin location for equivalent moments - = a ( ) R=+ C b a b D C D Equilibrium rigi boy oesn t eform coplanar force systems static: R R y y ( H) ( V) C ree oy Diagram D (sketch) tool to see all forces on a boy or a point incluing eternal forces weights force reactions eternal moments moment reactions internal forces Equilibrium 3 Lecture 5 Equilibrium 10 5

6 ree oy Diagram etermine boy REE it from: groun supports & connections raw all eternal forces acting ON the boy reactions applie forces gravity 100 lb + weight 100 lb mg ree oy Diagram sketch D with relevant geometry resolve each force into components known & unknown angles name them known & unknown forces name them known & unknown moments name them are any forces relate to other forces? for the unknowns write only as many equilibrium equations as neee solve up to 3 equations Equilibrium 11 Equilibrium 12 ree oy Diagram solve equations most times 1 unknown easily solve plug into other equation(s) common to have unknowns of force magnitues force angles moment magnitues Reactions on Rigi oies result of applying force unknown size connection or support type known irection relate to motion prevente no vertical motion no translation no translation no rotation Equilibrium 10 Lecture 5 Equilibrium 19 6

7 Supports an Connections Supports an Connections Equilibrium 20 Equilibrium 21 oment Equations sum moments at intersection where the most forces intersect multiple moment equations may not be useful combos: 0 y Concentrate Loas Equilibrium 21 Lecture 5 Loas 15 7

8 Distribute Loas eam Supports statically eterminate L L L simply supporte (most common) overhang cantilever statically ineterminate L continuous (most common case when L 1=L 2) L L L Proppe Restraine Loas 16 Internal eam orces 20 Lecture 12 Equivalent orce Systems replace forces by resultant place resultant where = 0 using calculus an area centrois y el W 0 L w loaing L loaing w() Loa reas area is with height of loa w is loa per unit length W is total loa w W w 0 W /2 /2 w W 2w 2 2 w w W 2/3 W/2 /3 /2 W/2 /6 /3 Loas 17 Lecture 9 Loas 19 Lecture 9 8

five moments ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2014 lecture ARCH 614

five moments ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2014 lecture ARCH 614 ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2014 lecture five moments Moments 1 Moments forces have the tendency to make a body rotate about an axis http://www.physics.umd.edu