Sideway
output.to from Sideway
Draft for Information Only

Engineering Mechanic Static

  1. Engineering Mechanics Statics

    Engineering Mechanics Statics is about forces in static equilibrium.
    http://output.to/sideway/default.asp?qno=110100001
     image
  2. Force

    Force is the resultant of interaction between two objects in the form of magnitude and direction at the point of interaction.
    http://output.to/sideway/default.asp?qno=110400006
     image
    1. Force of the resultant interaction at the point of interaction can either be combined or decomposed.
      http://output.to/sideway/default.asp?qno=110400005
       image
    2. The point of interaction is in static equilibrium when the resultant forces by Newton's first law of motion, acting on it is equal to zero.
      http://www.output.to/sideway/default.asp?qno=110400006
       image
    3. Force in a plane is just a special case of force in space with one rectangular force vector component equal to zero.
      http://www.output.to/sideway/default.asp?qno=110400005  
       image
    4. The vector representation of a force has the advantage of manipulating both the magnitude and direction of a force at the same time trigonometrically with the help of geometry especially in plane force manipulation.
      http://www.output.to/sideway/default.asp?qno=110400006  
       image
    5. Unit vectors, i, j, and k with unit magnitude are usually used to represent the directions of the three rectangular force vector components of a force in space after decomposition so that forces can be manipulated algebraically along the three axes of the coordinate system.
      http://www.output.to/sideway/default.asp?qno=110400005  
       image
    6. Direction cosines of a force which is equal to the cosines of θx, θy, and θz, are just the magnitude of the three rectangular force vector components of the unit vector λ along the force vector F and can be used to tackle problems with angles between the force vector and coordinate axes are known.
      http://www.output.to/sideway/default.asp?qno=110400005  
       image
  3. Free Body Diagram

    Free body diagram is one of the common techniques used in solving engineering mechanics statics problems by making use of the Newton's third law to isolate the interested area from the other parts of the whole system through the disconnection of the interaction between the interested area and the whole system at the idealized connection points.
    http://www.output.to/sideway/default.asp?qno=110100009  
     image
  4. Moment

    Moment of a force is the concept used to quantify the tendency to rotate an object about a reference point as the centre of moment when forces acting on the object are non-concurrent forces and is defined as product of force F along a line of action and perpendicular distance d as lever arm of rotation between line of action and point of reference, i.e. M=Fd=Frsinθ.
    http://www.output.to/sideway/default.asp?qno=110100009 
     image
    1. A moment vector following the right hand rule is usually used to represent the sense and axis of moment at the interested point for the additional effect due to a force acting on an object so that concepts of motion along the line of force and the tendency to rotate about a point can be handled separately.
      http://www.output.to/sideway/default.asp?qno=110100009  
       image
    2. When moment is treated as a vector quantity, moment vectors itself can be combined or decomposed through vector manipulation similar to force vector manipulation and the moment vector of a force about a point can also be obtained by the cross product operation of the position vector 𝐫 and the force vector 𝐅; i.e. 𝐌=𝐫⨯𝐅 or can be expressed in the determinant form.
      http://www.output.to/sideway/default.asp?qno=110600002   
       image
    3. Moment about point is tendency to rotate about axis along moment vector which is not always aligned with allowed rotation axis in practice, the moment about specified axis can be obtained by scalar product of unit vector 𝛌 along the specified axis passing through point O and moment 𝐌 of force 𝐅 about point O, i.e. 𝑀=𝛌⋅𝐌=𝛌⋅(𝐫⨯𝐅). or can be expressed in determinant form.
      http://www.output.to/sideway/default.asp?qno=110600003  
       image
  5. Moment Couple

    To eliminate limitations on using moment vector 𝐌 in static analysis, force couple concept is introduced such that moment effect due to force 𝐅 at point O is transformed into a free force couple vector of same magnitude and direction as moment vector but independent of force 𝐅 and point O since net force of force couple 𝐅₁𝐅₂ is zero, after translating force 𝐅 to point O.
    http://www.output.to/sideway/default.asp?qno=110600005 
     image
  6. System of Forces

    By the moment vector 𝐌 of force couple concept, system of forces acting on an object about the interested point O can be transformed into a resultant force vector 𝐑 by translating all forces 𝐅ᵢ to the interested point with moment effect is replaced by a free moment vector accordingly and a resultant moment vector 𝐌ₒ by vector addition of all free moment vectors 𝐌ᵢ.
    http://www.output.to/sideway/default.asp?qno=110700013 
     image
  7. Static Equilibrium

    An object is therefore in static equilibrium state only when both translational motion due to resultant force 𝐑 and rotational motion due to resultant moment 𝐌 are equal to zero.
    http://www.output.to/sideway/default.asp?qno=120200059 
     image
    1. By making use of free body diagram technique, an object can be any part of a mechanical system and since only six (three) equilibrium equations can be obtained from a rigid body in three (two) dimension no more than six (three) unknowns can be determined by the system of equilibrium equations and vector operation is the more convenient way to determine unknowns.
      http://www.output.to/sideway/default.asp?qno=120200067  
       image
  8. Structure Analysis

    Truss is an engineering structure with members in the truss are designed for supporting only axial loading of tensile and compressive force while bending moment is negligible and all jointed truss members can be considered as separated truss members with frictionless hinge pin joint as loads are always supported by the rigid three member triangular like structure.
    http://www.output.to/sideway/default.asp?qno=120200069  
     image
    1. Besides the forces in truss, the other two main concerns in truss design are stability and determinacy such that any unstable member arrangement and over rigid or constrained design are eliminated in the design.
      http://www.output.to/sideway/default.asp?qno=120200071  
       image
    2. Forces in trusses can be determined by method of joints through setting up two/three equilibrium equations for each point together with three/six static equilibrium equations to determine unknown reactions or by constructing force vector diagram with known forces and structure dimensions and therefore method of joints always start with joint with two/three unknown forces.
      http://www.output.to/sideway/default.asp?qno=120200072  
       image
    3. Forces in trusses can also be determined by method of sections through setting up three/six equilibrium equations for each virtual isolated section of truss with unlimited shape as a rigid body together with three/six static equilibrium equations to determine all unknown reactions and force vector diagram at joint may provide additional equilibrium equations also.
      http://www.output.to/sideway/default.asp?qno=120200074  
       image
    4. Frame is structure to support load similar to truss but with at least one multiple force member of more than two forces and all forces acting on the member are not along the direction of member axis and therefore unlike truss, although forces acting upon frame member can be determined similar to force analysis in truss, but unlike truss, moment should be considered also.
      http://www.output.to/sideway/default.asp?qno=120300010 
       image
    5. Machine is mechanical structure similar to frame but with moving component designed to transmit and modify forces and therefore a machine is usually a collapsible frame, but forces acting upon machine component can be determined similar to force analysis in frame member with the consideration of force and moment for each rigid component part.
      http://www.output.to/sideway/default.asp?qno=120300017
       image
  9. Distributed Force

    Besides the concentrated force which is represented by a force vector, the most common forces in practical problems are distributed forces which are either body forces acting over a volume or surface forces acting over an area and in general these distributed forces can also be represented by a concentrated force through system of forces transformation.
    http://www.output.to/sideway/default.asp?qno=120300021 
     image
    1. Body Forces

      Weight of a rigid object which can be considered as distributed body forces 𝐖ᵢ of infinitesimal element over a volume, can be represented by a single force 𝐖 through system of forces transformation and determined by equating the two systems of forces where the location of force is called centre of gravity which is same as the centroid of volume for a homogeneous body.
      http://www.output.to/sideway/default.asp?qno=120600009  
       image
    2. Surface Forces

      Similarly body dead load acting on a surface can be considered as distributed surface forces 𝐖ᵢ of infinitesimal element over surface normally which can be represented by a single force 𝐖 through system of forces transformation and determined by equating two systems of forces where location of force for a homogeneous distributed load depending on shape of load only.
      http://www.output.to/sideway/default.asp?qno=120700005 
       image
  10. Friction Force

    Besides distributed normal or inclined surface forces, friction force due to the relative lateral motion of two contact surfaces is a common distributed tangential surface force found in practical engineering problems and maximum static friction force which is proportional to the normal applied force can be developed when two surfaces are impending.
    http://www.output.to/sideway/default.asp?qno=120700007 
     image
  11. Internal Forces

    When a member of an rigid body is in static equilibrium, the internal forces in the member tending to resist those external forces should be in equilibrium similar to the structure analysis by section also but the internal force should be represented by a force-couple system instead of a force vector system since shear forces and bending moments are usually involved.
    http://www.output.to/sideway/default.asp?qno=120800020 
     image
  12. Second Moment

    In general, second moment of a body about a reference is the summation of moment of distributed forces of intensity proportional to the distance between force and reference over the body relating to the square or second order of distance and shape of the body only while first moment of a body about a reference is relating to the distance and shape of the body only.
    http://www.output.to/sideway/default.asp?qno=121000001 
     image
  13. Virtual Work

    When a body in static equilibrium, since all forces are in equilibrium and the resultant force on any particle is equal to zero, the work done by the resultant force is equal to zero also and therefore the work done on the particle for any virtual displacement δs is equal to zero as the resultant force acting on a particle is zero.
    http://www.output.to/sideway/default.asp?qno=121100089 
     image

©sideway

ID: 130800173 Last Updated: 8/20/2013 Revision: 0 Ref:

close

References

  1. I.C. Jong; B.G. rogers, 1991, Engineering Mechanics: Statics and Dynamics
  2. F.P. Beer; E.R. Johnston,Jr.; E.R. Eisenberg, 2004, Vector Mechanics for Engineers: Statics
close

Latest Updated LinksValid XHTML 1.0 Transitional Valid CSS!Nu Html Checker Firefox53 Chromena IExplorerna
IMAGE

Home 5

Business

Management

HBR 3

Information

Recreation

Hobbies 8

Culture

Chinese 1097

English 339

Reference 79

Computer

Hardware 249

Software

Application 213

Digitization 32

Latex 52

Manim 205

KB 1

Numeric 19

Programming

Web 289

Unicode 504

HTML 66

CSS 65

SVG 46

ASP.NET 270

OS 429

DeskTop 7

Python 72

Knowledge

Mathematics

Formulas 8

Algebra 84

Number Theory 206

Trigonometry 31

Geometry 34

Coordinate Geometry 2

Calculus 67

Complex Analysis 21

Engineering

Tables 8

Mechanical

Mechanics 1

Rigid Bodies

Statics 92

Dynamics 37

Fluid 5

Fluid Kinematics 5

Control

Process Control 1

Acoustics 19

FiniteElement 2

Natural Sciences

Matter 1

Electric 27

Biology 1

Geography 1


Copyright © 2000-2024 Sideway . All rights reserved Disclaimers last modified on 06 September 2019