SIMPLIFICATION OF FORCE AND COUPLE SYSTEMS
SIMPLIFICATION OF FORCE AND COUPLE SYSTEMSToday’s Objectives:Students will be able to:a) Determine the effect of moving aforce.b) Find an equivalent force-couplesystem for a system of forces andcouples.
READING QUIZ1. A general system of forces and couple moments acting on arigid body can be reduced to a .A) single forceB) single momentC) single force and two momentsD) single force and a single moment2. The original force and couple system and an equivalentforce-couple system have the same effect on a body.A) internalB) externalC) internal and externalD) microscopic
APPLICATIONSWhat are the resultant effects on the person’s handwhen the force is applied in these four different ways?Why is understanding these difference important whendesigning various load-bearing structures?
SIMPLIFICATION OF FORCE AND COUPLE SYSTEM(Section 4.7)When a number of forces and couplemoments are acting on a body, it iseasier to understand their overall effecton the body if they are combined into asingle force and couple moment havingthe same external effect.The two force and couple systems arecalled equivalent systems since theyhave the same external effect on thebody.
MOVING A FORCE ON ITS LINE OF ACTIONMoving a force from A to B, when both points are on thevector’s line of action, does not change the external effect.Hence, a force vector is called a sliding vector. (But theinternal effect of the force on the body does depend on wherethe force is applied).
MOVING A FORCE OFF OF ITS LINE OF ACTIONBWhen a force is moved, but not along its line of action, there isa change in its external effect!Essentially, moving a force from point A to B (as shown above)requires creating an additional couple moment. So moving aforce means you have to “add” a new couple.Since this new couple moment is a “free” vector, it can beapplied at any point on the body.
SIMPLIFICATION OF A FORCE AND COUPLE SYSTEMWhen several forces and couple momentsact on a body, you can move each forceand its associated couple moment to acommon point O.Now you can add all the forces andcouple moments together and find oneresultant force-couple moment pair.
SIMPLIFICATION OF A FORCE AND COUPLE SYSTEM(continued)WR W1 W2(MR)o W1 d1 W2 d2If the force system lies in the x-y plane (a 2-D case), then thereduced equivalent system can be obtained using the followingthree scalar equations.
EXAMPLE #1Given: A 2-D force systemwith geometry as shown.Find: The equivalent resultantforce and couplemoment acting at APlan:1) Sum all the x and y components of the forces to find FRA.2) Find and sum all the moments resulting from moving eachforce component to A.
MRAFREXAMPLE #1(continued) ΣFRx 150 (3/5) 50 –100 (4/5) 60 lb ΣFRy 150 (4/5) 100 (3/5) 180 lb MRA 100 (4/5) 1 – 100 (3/5) 6– 150(4/5) 3 – 640 lb·ftFR ( 602 1802 )1/2 190 lbθ tan-1 ( 180/60) 71.6
GROUP PROBLEM SOLVINGGiven: A 2-D force and couplesystem as shown.Find: The equivalent resultantforce and couplemoment acting at A.Plan:1) Sum all the x and y components of the two forces to find FRA.2) Find and sum all the moments resulting from moving eachforce to A and add them to the 45 kN m free moment to findthe resultant MRA .
GROUP PROBLEM SOLVING (continued)Summing the force components: ΣFx (5/13) 26 – 30 sin 30 – 5 kN ΣFy – (12/13) 26 – 30 cos 30 – 49.98 kNNow find the magnitude and direction of the resultant.FRA ( 5 2 49.98 2 )1/2 50.2 kN and θ tan-1 (49.98/5) 84.3 MRA {30 sin 30 (0.3m) – 30 cos 30 (2m) – (5/13) 26 (0.3m)– (12/13) 26 (6m) – 45 } – 239 kN m
ATTENTION QUIZ1. For this force system, the equivalent system at P is.A) FRP 40 lb (along x-dir.) and MRP 60 ft ·lbB) FRP 0 lb and MRP 30 ft · lbC) FRP 30 lb (along y-dir.) and MRP -30 ft ·lbD) FRP 40 lb (along x-dir.) and MRP 30 ft ·lby1'1' P30 lb40 lb30 lbx
a change in its external effect! B Essentially, moving a force from point A to B (as shown above) requires creating an additional couple moment. So moving a force means you have to “add” a new couple. Since this new couple moment is a “
a change in its external effect! Essentially, moving a force from point A to B (as shown above) requires creating an additional couple moment. So moving a force means you have to “add” a new couple. Since this new couple moment is a “fr
STATIC FORCE ANALYSIS WEEK 1 . COUPLE MOMENT OF COUPLE Couple: Two equal and opposite forces (F & F’) Moment of Couple: A vector normal to the plane of the couple (M R BA X F) Conditions of Equilibrium A system of bodies is
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