is concerned with the basic principles of the Universe. ▫ is one of the his Principia. ▫. Today, mechanics is of vital inportance to students from all disciplines. Worked Examples from Introductory Physics. Vol. I: Basic Mechanics. David Murdock. Tenn. Tech. Univ. February 24, FLUID MECHANICS. Fluid statics. Equations of fluid motion. Bernoulli's equation. Conservation of mass. Viscous effects.

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Basic mechanics. Basic principles of statics. Statics is the branch of mechanics that deals with the equilibrium of stationary bodies under the action of forces. Mechanics is that branch of science which deals with the forces and their effects units: The basic quantities or fundamental quantities of mechanics are those. Basic principles: Equivalent force system; Equations of equilibrium; Free R. C. Hibbler, Engineering Mechanics: Principles of Statics and Dynamics, Pearson.

In mechanics. The moment of inertia about the x-x axis of such a strip is the area of the strip multiplied by the square of the perpendicular distance from its centroid to the x-x axis. Critical points are: This in turn enables the force vector diagram to be drawn. Moments of forces The effect of a force on a rigid body depends on its point of application. At the bottom. These two transverse sections are the two most likely points for failure in shear.

As we approach the right-hand end of the beam we find the mathematics easier to consider on the right-hand side of any section. Critical points are: Calculate the values of the shear force to the left and to the right of all critical points. These two transverse sections are the two most likely points for failure in shear.

One is at E and the other is between H and G. Calculate values of the bending moment at all critical points. It is the effect that one load would have on the bent shape at the chosen point that determines the sign.

When designing beams in materials such as concrete. The bending moment at G is obviously zero 5. Critical points for bending moment are: Chapter 6 — Basic mechanics The shear-force diagram in the example has two points where the shear force is zero.

At point H we have the maximum bending moment: For the calculation of primary stresses. The force can be a pure tension conventionally designated positive. It will read a value of zero after 2. For the bending moment at F consider the loads to the right of this point.

If the inclusion of other points would be helpful in drawing the curve. These are internal forces that must be in equilibrium with the external applied forces. The variation of the bending moment under a UDL is parabolic 7. Values of bending moment are calculated using the definition and sign convention.

Positive bending moments sagging cause compression in the top fibres of the beam. Method of sections: The free-body diagram considered is for a portion of the framework to one side or the other of a cut section.

Joint analysis: This is based on considering the equilibrium of each joint in turn and using the freebody diagram for each joint. Application of the equations of equilibrium will solve the unknown forces in the cut section. The members GH and HB are therefore in tension.

This is also called a Pascal Pa. This provides an analytical solution and is most useful when requiring the answers for one or two members only.

The forces in the members cut by the section are included in the free-body diagram. As the effect of the force is distributed over the crosssection area of the body. Although these deformations are seldom visible to the naked eye. If the loads are large enough. If the bar were to fail in tension. The load is spread uniformly over the top of the pier.

This limiting value of stress is called the elastic limit. This is called the modulus of elasticity. Two gauge points are marked on the rod and the distance between them is measured after each force increment has been added.

The modulus of elasticity will have the same units as stress Pa. The rod is hung vertically and a series of forces are applied at the lower end. A convenient way of demonstrating elastic behaviour is to plot a graph of the results of a simple tensile test carried out on a thin mild steel rod.

In many cases. How much will they shorten because of the load? The slope of this straight line is the constant of proportionality. Within the elastic range. This is because strain has no units. If the stress is steadily increased. Although there are always small deformations present in the other two dimensions. In farm structures. The test is continued until the rod breaks. Dynamic loading results from a change of loading. Imposed loads include earthquake loads. Very often wind loading proves to be the most critical load imposed on agricultural buildings.

Not all the imposed loads will necessarily reach their maximum values at the same time. For example. The value of the factor of safety has to be chosen with a variety of conditions in mind. Wind loads are imposed loads. For these and other reasons.

When designing a structure. Common loadings are those that occur frequently. Wind loads are naturally dependent on wind speed. In this case. In some cases for example. Other materials. Hence estimates of self-weight of some members must be made before commencing a design analysis and the values checked upon completion of the design.

Chapter 6 — Basic mechanics Also. Structural design is not an exact science and. Imposed loads are loads related to the use of the structure and to the environmental conditions. Dead loads are loads resulting from the selfweight of all permanent construction.

This margin is called the factor of safety. The self-weight of some parts of a structure. In the case of building materials such as steel and timber.

Loads are not transmitted as such. In a rod or a bar under axial tension.

The choice of material for a member may be influenced to some extent by the type of loading. Ties and struts When bars are connected with pin joints and the resulting structure loaded at the joints. X Column Z Y X Primary load effects A primary load effect is defined as being the direct result of a force or a moment. Rods or bars under compression are the basis for vertical structural elements such as columns. They may be loaded axially or they may have to be designed to resist bending when the load is eccentric.

The members are subjected only to axial loads and members in tension are called ties. Standard case values of shear force. In most cases. It is usual practice to orientate the Cartesian z-z axis along the length of the member and the x-x and y-y axes along the horizontal and vertical cross-sectional axes respectively.

Any single load or combination of loads can give rise to one or more of these primary load effects. In more complex situations.

Secondary load effects. They are often used to transfer load effects from beams. For instance. Z Y Rod Rods. Cables are the most efficient structural elements because they allow every fibre of the crosssection to resist the applied loads up to any allowable stress. To a degree. Arches exert vertical and horizontal thrusts on their supports. The span that a beam can usefully cover is limited by the self-weight of the beam.

Their magnitudes will vary along. This problem of horizontal thrust can be eliminated by connecting a tension member between the support points. The safe span for long. T Web Flanges Beam A beam is a member used to resist a load acting across its longitudinal axis by transferring the effect over a distance between supports — referred to as the span.

Sp an Simple arch Built. Hallow web beam Arch The arch can be shaped such that. Internal forces at any cross-section of the plane frame member are: The moment of inertia about the x-x axis of such a strip is the area of the strip multiplied by the square of the perpendicular distance from its centroid to the x-x axis. By applying calculus and integrating as follows. Calculation of moment of inertia Consider a rectangle that consists of an infinite number of strips.

Note that the centroid is sometimes outside the actual cross-section of the structural element. The best shape for a section is one that has the greater part of its area as distant as possible from its centroidal. Other factors. The moment of inertia measures only how the geometric properties or shape of a section affect its value as a beam or slender column. For design purposes. The area moment of inertia I.. The entire cross-section of both the beam and the cross-section of the web have their centroids on the x-x axis.

Principle of parallel axes According to the principle of parallel axes. Some examples are given in Appendix V. Determine the moment of inertia about the x-x axis and the y-y axis for the I-beam shown in the figure.

It is the ratio of the moment of inertia I about the neutral axis of the section to the distance C from the neutral axis to the edge of the section. For structural rolled-steel sections.

In structural design. Slender compression members tend to buckle about the axis for which the radius of gyration is a minimum value.

From the equations. AVI Book Co. Sketch the shear and bending moment diagrams for the beams below. Nath Market. New Delhi. Find the position of the section that has to support the greatest bending moment. Fundamentals of structural analysis with computer analysis and applications.

Englewood Cliffs. Structural mechanics: Khanna Publishers. New Jersey. Structure in architecture: Find the reactions on beam BC. Materials and structures. Chand and Company Ltd. Pearson Education. Light agricultural and industrial structures: A text book of strength of materials.

New York. Ram Nagar. Chapter 6 — Basic mechanics review qUestions 1. Nai Sarak. Obtain an expression for the maximum bending moment at a section of the girder at a distance of z metres from an abutment. Basic Mechanics Uploaded by Ratna Kommoji.

Flag for inappropriate content. Related titles. SCF equations in multi-planar welded tubular DT-joints including bending effects. End region prestressed beam-Phoenix-corrections. Jump to Page. Search inside document. P force A force is defined as any cause that tends to alter the state of rest of a body or its state of uniform motion in a straight line.

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