Free body diagrams

When analysing meehanieal systems, it is usual to identify all external forees by the use of a Free-body diagram , and then apply Newton s seeond law of motion in the form ... 

Fig. 2.6 Free-body diagram for spring-mass-damper system.

Using equations (2.12) and (2.14) the free-body diagram is shown in Figure 2.6. From equation (2.18), the equation of motion is... 

Fig. 2.9 Free-body diagrams for reduction gearbox. Gearbox parameters...

The free-body diagrams for the motor shaft and output shaft are shown in Figure 2.9. Equations of Motion are... 

Fig. 4.21 Free-body diagram of load on hydraulic actuator.

Gearbox, lead-screw and machine-table. With reference to Figure 2.9 (free-body diagram of a gearbox), the motor-shaft will have zero viscous friction Cm, hence equation (2.22), using Laplace notation, becomes... 

The output shaft in this case is the lead screw, which is assumed to have zero moment of inertia /q and viscous friction Cq. The free-body diagrams of the machine-table and lead-screw are shown in Figure 4.30. 

Fig. 4.30 Free-body diagrams of lead-screw and machine-table.

Figure 4.36 shows the hull free-body diagram. Disturbance effects (wind, waves and current) are not included. 

Fig. 4.36 Free-body diagram of ship hull dynamics.

Fig. 8.1 Spring-mass-damper system and free-body diagram.

Irrespective of the analysis approach, the representative volume element must be carefully defined and used. In fact, the representative volume element is crucial to the analysis and is the micromechanics analog of the free-body diagram in statics and dynamics. The representative volume element is of higher order than the free-body diagram because deformations and stresses are addressed in addition to forces. 

Figure 4-51 Free-Body Diagram for an Angle-Ply Laminate 4.6.2 Elasticity Formulation...

Figure 4-57 Free-Body Diagram for Cross-Ply Laminate...

Figure D-1 Free-Body Diagram of a Beam Element...

Thus, solving a problem in particle statics reduces to finding the unknown force or forces such that the resultant force will be zero. To facilitate this process it is useful to draw a diagram showing the particle of interest and all the forces acting upon it. This is called a free-body diagram. Next a coordinate system (usually Cartesian) is superimposed on the free-body diagram, and tbe force.s are decomposed into their... 

It is often necessary to compute the forces in structures made up of connected rigid bodies. A free-body diagram of the entire structure is used to develop an equation or equations of equilibrium based on the body weight of the structure and the external forces. Then the structure is decomposed into its elements and equilibrium equations are written for each element, taking advantage of the fact that by Newton s third law the forces between two members at a common frictionless joint are equal and opposite. 

Applications of Newton s Second Law. Problems involving no unbalanced couples can often be solved with the second law and the principles of kinematics. As in statics, it is appropriate to start with a free-body diagram showing all forces, decompose the forces into their components along a convenient set of orthogonal coordinate axes, and then solve a set of algebraic equations in each coordinate direction. If the accelerations are known, the solution will be for an unknown force or forces, and if the forces are known the solution will be for an unknown acceleration or accelerations. 

As shown in the free-body diagram of Figure 2-15b, all the motion of the block is parallel to the surface of the ramp thus there is a static force balance in the y direction. 

In Figure 2-16 a 10 lb cylinder with a 3-in. radius rolls down a 30° incline. What is its angular acceleration and the linear acceleration of its center of mass In the free-body diagram of Figure 2-16, the point of contact between the wheel and the ramp is the instantaneous center of zero velocity. Thus,... 

A beam subjected to a simple transverse load (Figure 2-29a) will bend. Furthermore, if the beam is cut (Figure 2-29b) and free body diagrams of the remaining sections are constructed, then a shear force V and a moment M must be applied to the cut ends to maintain static equilibrium. 

FTMA provides a direct method for determining the frequency at which inertial effects become noticeable. For this purpose the outer mount is detached from the "rigid" foundation and the accelerometer is mounted on it. The free body diagram of the outer mount-accelerometer assembly is shown in Figure 4. The relevant equation of motion is... 

FREE BODY DIAGRAM OF POLYMER-OUTER MOUNT-ACCELEROMETER ASSEMBLY... 

FIGURE 6.8 Bubble free-body diagrams to illustrate power dissipation. 

FIGURE 7.10 Free-body diagram of a cylinder (pipe) of fluid and bed material. 

Free-body diagram of a fluid disk element of radius R and length tit in fully developed laminar flow in a horizontal lube. 

Fig. 11.23. Free-body diagram for the interaction of a dislocation and an obstacle characterized by a pinning force F.

I am, and ever will be, a white-socks, pocket-protector, nerdy engineer — born under the second law of thermodynamics, steeped in the steam tables, in love with free-body diagrams, transformed by Laplace, and propelled by compressible flow... dedicated to doing things better and more efficiently [1],... 

FEA is fundamentally based on static equilibrium principles. The sum of all forces in any direction and the sum of all moments about any axis are zero. In a static analysis, the dynamic aspect of the load is ignored. As in static analysis, a free body diagram (FBD) is used. An FBD gives a picture of the part with the loads and moments represented graphically. For any point, there are six degrees of freedom three translations along each axis and three rotations about each axis. In static equilibrium, the sum of all forces in any direction and the sum of all moments about any axis are zero. In static analysis the dynamic aspect of the load is ignored. 

FBDs are important in analysis because they allow visualization of the things that are felt by the part but not shown on the screen. FEA has its roots in truss analysis, where each member of the truss carries only axial load transmitted from someplace else on the truss. The free body diagram is a sketch of each element in isolation, showing force arrows where they occur at the pins and supports. The equilibrium equation is... 

The free body diagram will break down these truss models into its individual members and analyze which type of force or moment is acting upon each member at each node, or point. Figure 4.10 shows the FBD of the simple loaded truss it shows if the member is in compression or tension (stretching) and shows the force designated (P) on each member. 

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