ENGR-36_Lec-07_Moments_Intro.ppt 1 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 36 Chp 4: Intro to Moments

ENGR-36_Lec-07_Moments_Intro.ppt 2 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Moment (Torque) Described  In Physics and Engineering a MOMENT is a measure of TWISTING Power  The MAGNITUDE of a Moment is the PRODUCT of a Lever Arm Distance and an Intensity The “Intensity” can be a Force, an Electric Charge, an Area, a Mass, or other In Engineering Mechanics the Intensity takes the form of a Force

ENGR-36_Lec-07_Moments_Intro.ppt 3 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Moment Described  In General, MOMENTS are VECTOR Quantities with Magnitude (see previous slide) and Direction  The Direction of the Moment Vector is determined by the Right Hand Rule Wrap Fingers in the Direction of ROTATION (or tendency to rotate), then THUMB points in the Direction of the Moment Vector

ENGR-36_Lec-07_Moments_Intro.ppt 4 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Moment Center  The MOMENT CENTER is equivalent to the PIVOT POINT about which Rotation would occur upon application of a Force whose Line of Action is OFFSET from the Pivot Point Moment Center (MC) or Pivot Point  distance from the Pivot to Force Loa

ENGR-36_Lec-07_Moments_Intro.ppt 5 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Position Vector  The Position Vector runs from the Moment Center to ANY Point on the LoA of the Force Often times the most Convenient Point on the LoA is the Point of Application (PoA) –i.e., Pos. Vector runs from the Pivot to the PoA  The position Vector Contains within it the “LeverArm” part of the Moment Calc

ENGR-36_Lec-07_Moments_Intro.ppt 6 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Picking the Position Vector, r  Often the Most Convenient Position Vector is that which runs From the Pivot to the Point of Application r runs from the Pivot to the Point  OTHER Pts on the Force LoA may be more easily determined and are thus More Convenient

ENGR-36_Lec-07_Moments_Intro.ppt 7 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Shortest Position Vector  The Shortest vector is that which is  to the Force LoA  The Mag of the Shortest r is called the Perpendicular Distance, d:  distance yields Shortest r

ENGR-36_Lec-07_Moments_Intro.ppt 8 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Moment Magnitude  As Noted Previously the Magnitude of a Moment is related to the product of The Position Vector, r The Force, F  Mathematically Thus knowing F & d allows Calc of the Moment magnitude, but NOT its SENSE (direction)

ENGR-36_Lec-07_Moments_Intro.ppt 9 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Moment Sense  TWO-DIMENSIONAL STRUCTURES Have Length And Breadth But Negligible Depth And Are Subjected To Forces Contained In The PLANE Of The Structure  The Plane Of The Structure Contains The Point O And The Force F. M O, The Moment Of The Force About O Is Perpendicular To The Plane.

ENGR-36_Lec-07_Moments_Intro.ppt 10 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Moment Sense/Direction  If The Force Tends To Rotate The Structure CLOCKWISE, The Sense Of The Moment Vector Is INTO The Structure Plane SIGN{M O } → NEGATIVE  If The Force Tends To Rotate The Structure COUNTER-clockwise, The Sense Of The Moment Vector Is OUT Of The Structure Plane SIGN{M O } → POSITIVE

ENGR-36_Lec-07_Moments_Intro.ppt 11 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Moment Direction by Rt Hand Rule 1.Point Fingers in r Direction 2.Curl Fingers Toward +F Direction 3.THUMB Points in the Direction of M HINT: Put r & F Tail-to-Tail r F

ENGR-36_Lec-07_Moments_Intro.ppt 12 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Moments Point in ALL Directions  Since r and F can be arbitrarily oriented relative to the CoOrd Axes, then M will also be arbitrarily Oriented Confirm These using your own Right Hand

ENGR-36_Lec-07_Moments_Intro.ppt 13 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Moment Units  Force Dist  Discern the UNITS for Moments from  Typical Units Ft-lbs In-lbs N-m N-mm

ENGR-36_Lec-07_Moments_Intro.ppt 14 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example: Moment Calculation  A 100-lb Vertical Force Is Applied To The End Of A Lever Which Is Attached To a Shaft At O. DETERMINE a)Moment About O b)Horizontal Force At Pt-A Which Creates The SAME Moment c)Smallest Force At Pt-A Which Produces The SAME Moment d)Location For a 240-lb Vertical Force To Produce The SAME Moment e)Whether Any Of The Forces From b, c, and d is EQUIVALENT To The ORIGINAL Force

ENGR-36_Lec-07_Moments_Intro.ppt 15 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example M Calc – Soln (a)  Moment About O Is Equal To The Product Of The Force And The PERPENDICULAR DISTANCE Between The Line Of Action Of The Force And O  The Force Tends To Rotate The Lever CLOCKWISE, Thus The Moment Vector points INTO The Plane Of The Paper The Moment Vector Qty is thus NEGATIVE

ENGR-36_Lec-07_Moments_Intro.ppt 16 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example M Calc – Soln (b)  Horizontal Force at A That Produces The Same Moment

ENGR-36_Lec-07_Moments_Intro.ppt 17 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example M Calc – Soln (c)  The Smallest Force at A To Produce The Same Moment Occurs When The Perpendicular Distance is a Maximum i.e., When F Is Perpendicular To OA

ENGR-36_Lec-07_Moments_Intro.ppt 18 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example M Calc – Soln (d)  To Determine The Point Of Application Of A 240 lb Vertical Force To Produce The Same Moment

ENGR-36_Lec-07_Moments_Intro.ppt 19 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example M Calc – Soln (e)  Although Each Of The Forces In Parts b), c), and d) Produces The Same Moment As The 100 lb Force, NONE Are of The Same MAGNITUDE And SENSE (Line of Action) as the original pull  NONE Of The Forces Is Equivalent To The 100 lb force

ENGR-36_Lec-07_Moments_Intro.ppt 20 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics WhiteBoard Work Let’s Work Problem 4.21 In order to pull out the nail at B, the force F exerted on the handle of the hammer must produce a clockwise moment of 500 in∙lb. about point A. Determine the required magnitude of force F.

ENGR-36_Lec-07_Moments_Intro.ppt 21 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR-36_Lec-07_Moments_Intro.ppt 22 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR-36_Lec-07_Moments_Intro.ppt 23 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR-36_Lec-07_Moments_Intro.ppt 24 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 36 Appendix