Report

Engineering 36 Chp 5: FBDs 2D/3D Systems Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected] Engineering-36: Engineering Mechanics - Statics 1 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Free Body Diagrams (FBDs) A free-body diagram is a sketch of an object of interest with all the surrounding objects stripped away to reveal all of the forces acting on the body Engineering-36: Engineering Mechanics - Statics 2 Free Body Diagram Space Diagram The purpose of a free-body force diagram is to assist with determination of the Net Force and/or Moment acting on a body Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Constructing a free-body diagram Select an object or group of objects to focus on as the "body“: i.e., the system. Sketch the body by itself, "free" of its surroundings Draw only those forces/moments that are acting directly on the body. • Include both the magnitude and the direction of these forces. Do not include any forces that the body exerts on it surroundings, they do NOT act ON the body. • However, there is always an equal reaction force acting on the body. For a compound body (e.g. Trusses, Machines) you do NOT need to include any INTERNAL forces acting between the body's SUBPARTS • these internal forces come in action-reaction pairs which cancel out each other because of Newton's Third Law. Choose a coordinate system and sketch it on the free-body diagram. Often choose one of the axes to be parallel one or more forces • it can sometimes simplify the equations to be solved. Engineering-36: Engineering Mechanics - Statics 3 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Structural Supports NonMoving Structures are typically Connected to Some Sort of Supporting Base The connection between the Structure and Base are usually Called “Structural Supports” The Force and/or moments exerted on the Structure Base are usually called “Structural Reactions” (RCNs for Short) Engineering-36: Engineering Mechanics - Statics 4 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Structural Supports A Support that Prevents Linear Motion (sliding, translating) of the structure then exerts a Force on the structure A Support that Prevents Rotating Motion (twisting, turning) of the structure then exerts a Couple Moment on the structure Engineering-36: Engineering Mechanics - Statics 5 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Recall SLIDING & FREE Vectors Forces are SLIDING Vectors; They can applied at ANY-POINT on the Vector Line of Action (LoA) COUPLE-Moments are FREE Vectors; They can be applied at ANY Point, On or Off the Body Engineering-36: Engineering Mechanics - Statics 6 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 2D Support ReActions Cable can only Generate TENSION WeightLess Link is 2-Force Element Engineering-36: Engineering Mechanics - Statics 7 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 2D Support ReActions Note that in BOTH these Cases the Support ReAction is NORMAL (Perpendicular) to the Supporting Surface RCN can only PUSH, and NOT PULL Engineering-36: Engineering Mechanics - Statics 8 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 2D Support ReActions Note that in BOTH these Cases the Support ReAction is NORMAL (Perpendicular) to the Supporting Surface RCN can PUSH or PULL Engineering-36: Engineering Mechanics - Statics 9 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 2D Support ReActions Only the Supports (9) & (10) Can Generate a Couple-Moment ReAction Engineering-36: Engineering Mechanics - Statics 10 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Center of Gravity If the Weight of the Rigid Body is Not Negligible, then the Entire Weight of the Body can be concentrated at a Single Point Called the Center of Gravity (CG) • Many times the CG location is Given – Can Calculate using Centroid Methods which will be covered later Engineering-36: Engineering Mechanics - Statics 11 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 2D Free-Body Diagram First Steps for Static Rigid-Body Equilibrium Analysis • Identification of All Forces & Moments Acting on the Body • Formulation of the Free-Body Diagram Free Body Diagram Construction Process • See next slide Engineering-36: Engineering Mechanics - Statics 12 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 2D Free-Body Diagram cont 1. Select the extent of the free-body and detach it from the ground and other bodies 2. Indicate for external loads: • • Point of application Magnitude & Direction Of External Forces – Including The Body Weight. 3. Indicate point of application and ASSUMED direction of UNKNOWN applied forces Engineering-36: Engineering Mechanics - Statics 13 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 2D Free-Body Diagram cont.2 • The Unknown Forces Typically Include REACTIONS through which the GROUND and OTHER BODIES oppose the possible motion of the rigid body 4. Include All dimensions Needed to Calculate the Moments of the Forces Engineering-36: Engineering Mechanics - Statics 14 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Example: Truss Structure Consider Rocker & Pin Supported Truss Analyze Loading • Four External Force Loads as shown • Truss Weight, W • RCN at Pt-A by Rocker – Expect NORMAL to support Pad • RCN at Pt-B by Pin Draw the FBD for this Structure Engineering-36: Engineering Mechanics - Statics 15 – Expect in plane of Truss Arbitrarily Directed Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Example: Truss – Draw FBD This Dwg is, in fact, a Full Free Body Diagram RBx RA W Engineering-36: Engineering Mechanics - Statics 16 RBy RB φ Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 3D Support ReActions Same as 2D ReActions of this Type Engineering-36: Engineering Mechanics - Statics 17 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 3D Support ReActions Ball-n-Socket is the 3D analog to the 2D Smooth Pin or Hinge Engineering-36: Engineering Mechanics - Statics 18 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 3D Support ReActions This configuration is Commonly Known as a “Pillow Block Bearing”. Type of support is (obviously) designed to allow the shaft to SPIN FREELY on its AXIS Engineering-36: Engineering Mechanics - Statics 19 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 3D Support ReActions The Sq-Shaft Bearing System does NOT Allow the shaft to spin completely freely, Thus the My Engineering-36: Engineering Mechanics - Statics 20 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 3D Support ReActions These supports are (obviously) designed to allow the Free Spin on the Pin Axis Engineering-36: Engineering Mechanics - Statics 21 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx 3D Support ReActions This Type of support is commonly Known as a CANTILEVER. • Generates the Maximum Amount of Unknowns for 3D systems Engineering-36: Engineering Mechanics - Statics 22 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx ROUGH SURFACE ReActions Friction on a Rough Surface will Generate RCNs Parallel to the Supporting Surface • 2D • 3D Engineering-36: Engineering Mechanics - Statics 23 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Example: Hinge & Rough-Surf Given Bar supported by Hinge at Pt-A and rests on the Rough x*y*z* Surface at Pt-B Engineering-36: Engineering Mechanics - Statics 24 Analyze Rcn at Pt-A. By 5.2-(9) the Single Axially Constrained Hinge will • Provide Lateral (y & z) and Axial (x) Support • Resist twisting about the y and z axes Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Example: Hinge & Rough-Surf PUSH (not PULL) Normal to the Surface • In this case the y* direction is normal to the supporting plane Resist Sliding in any direction WITHIN Analyze Rcn at Pt-B. the supporting plane Support Leg on a rough surface will Engineering-36: Engineering Mechanics - Statics 25 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Example: cont. FAx MAy • If the Weight of the Bar is negligible, then All Forces are accounted for and this is, in fact, the FBD FAy FAz FBz* MAz FBx* Engineering-36: Engineering Mechanics - Statics 26 FBy* Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Symmetry City If We’re Lucky enough to have a Plane of Symmetry for BOTH Loading and Structural GEOMETRY then we can treat real world 3D problems as 2D • OtherWise we need to Operate in full 3D No Symmetry Can Treat as 2D Engineering-36: Engineering Mechanics - Statics 27 Must Treat as 3D Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Example: Utility Pole Consider Leaning Utility Pole Determine the Loads acting on the BASE of the Pole Analyze Rcn at Base • This is a FIXED support which is often call a CantiLever • Cantilever supports resist both forces and moments in ALL 3 Spatial Directions Engineering-36: Engineering Mechanics - Statics 28 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Example: Pole Draw in the BASE ReActions This Diagram is NOT a FBD as it does not account for these forces acting on the pole • Pole Weight • Cable Tension MAx FAx MAy FAy FAz MAz Engineering-36: Engineering Mechanics - Statics 29 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Distributed Forces/Loads In Some Cases Forces are concentrated at Points; this is simplest case Often times a Load cannot be identified with a single point; Instead the Load is Spread Out over a supporting surface • Such Forces are Called “Distributed” Distributed Loads are indicated with a Load Profile Engineering-36: Engineering Mechanics - Statics 30 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Distributed Force Profiles A uniformily Dist Load Has the same action at every point on it’s region of application. • It’s profile is “Flat” NonUniform Loads are also common • They may be kinked, curved, or arbitrary Engineering-36: Engineering Mechanics - Statics 31 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Distributed-Force Equivalent In Chp4 we discussed how to Replace a Distributed-Load with an Equivalent Point-Load placed at a Specific Location Units for Distributed Forces • 2D → Force per Length (lb/ft, lb/in N/m) • 3D → Force Per Area (Pa, PSI, PSF) Engineering-36: Engineering Mechanics - Statics 32 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Example: Hydraulic Cylinder The Hydraulic Cylinder Pumps Fluid in & out of the Cylinder Reservoir as Shown at Right Draw The loads on the Piston Assy Game Plan: • Isolate Piston Assy as Free Body • CareFully Account for all Pt-Force and PRESSURES acting on the Piston Assy Engineering-36: Engineering Mechanics - Statics 33 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Example – Cont. Load-1 = 100 kg (220lb, 9.81kN) CounterWt FOr Load-2 = Weight of the Piston Rod Load-3 = Weight of the Piston WP WR Load-4 = Lateral Restraining Forces Exerted by the Cylinder Wall on the O-Ring 9.81kN Engineering-36: Engineering Mechanics - Statics 34 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx FOr Pair Example – Cont. Load-5 = The Air Pressure on Top of the Piston Load-6 = The Hydraulic Fluid Pressure on the Bottom of the Cylinder FOr WP Pfluid WR 9.81kN Engineering-36: Engineering Mechanics - Statics 35 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx FOr Pair Example – Cont. We can SIMPLIFY the analysis by making assessments about the relative significance of the loads • The Weight of the Rod and Piston are likely negligible compared to the Counter Weight FOr WP Pfluid WR 9.81kN Engineering-36: Engineering Mechanics - Statics 36 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx FOr Pair Example – Cont. FOr Additional Symplifications • The SideWall Forces on the O-Ring must cancel if the Cylinder is Balanced FOr Pfluid • The AIR pressure is negligible compared to the FLUID pressure 9.81kN Engineering-36: Engineering Mechanics - Statics 37 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Example – Cont. Thus in the NonMoving Simplified System the Fluid Pressure balances the Counter Weight. Pfluid Mathematically Pfluid Area piston 9.81 kN 9.81kN Engineering-36: Engineering Mechanics - Statics 38 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx WhiteBoard Work None Today; Did by PowerPoint A C 47° 57° D 7 kN B W Engineering-36: Engineering Mechanics - Statics 39 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx Engineering 36 Appendix Bruce Mayer, PE Registered Electrical & Mechanical Engineer [email protected] Engineering-36: Engineering Mechanics - Statics 40 Bruce Mayer, PE [email protected] • ENGR-36_Lec-10_FBDs_2D_3D_Systems.pptx