# ENGINEERING MECHANICS SHAMES PDF

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Irving H Shames Engineering Mechanics that is written by sppn.info Study can be reviewed or downloaded through word, ppt, pdf. Engineering Mechanics By sppn.info - Free download Ebook, Handbook, Textbook, User Pdf Shames Fluid Mechanics Solution Engineering Mechanics . Mechanics - Statics and Dynamics Fourth Edition, by Irving H. Prentice Hall of India Pvt. shames engineering mechanics pdf free download sppn.infoering.

The rotation of the earth gives rise to an event that serves as a good measure of time-the day. But we need smaller units in most of our work in engineering, and thus, generally, we tie events to the second, which is an interval repeatable 86, times a day.

Mass-A Property of Matter. The student ordinarily has no trouble under- standing the concepts of length and time because helshe is constantly aware of the size of things through hisher senses of sight and touch, and is always conscious of time by observing the flow of events in hisher daily life. The concept of mass, however, is not as easily grasped since it does not impinge as directly on our daily experience.

Mass is a property of matter that can be determined from two different actions on bodies.

## Irving H. Shames-Engineering Mechanics (Statics and Dynamics).()

To study the first action, suppose that we consider two hard bodies of entirely different composition, size, shape, color, and so on. If we attach the bodies to identical springs, as shown in Fig.

By grinding off some of the material on the body that causes the greater extension, we can make the deflections that are induced on both springs Figure 1. Bodies restrained by identical equal. Even if we raise the springs to a new height above the earths surface, springs. And since they are, we can conclude that the bodies have an equivalent innate property. This property of each body that manifests itself in the amount of gravitational attraction we call man. The equivalence of these bodies, after the aforementioned grinding oper- ation, can be indicated in yet a second action.

If we move both bodies an equal distance downward, by stretching each spring, and then release them at the same time, they will begin to move in an identical manner except for small variations due to differences in wind friction and local deformations of the bodies. We have imposed, in effect, the same mechanical disturbance on each body and we have elicited the same dynamical response. Hence, despite many obvious differences, the two bodies again show an equivalence.

The two basic units commonly used in much American engineering practice to measure mass are the pound mass, which is defined in terms of the attraction of gravity for a standard body at a standard location, and the slug, which is defined in terms of the dynamical response of a stan- dard body to a standard mechanical disturbance.

A similar duality of mass units does not exist in the SI system. There only the kilugmm is used as the basic measure of mass. Resolve thc h force into a set of components along the slot shown and in the vertical direction. If the forces in the members are colinear with the mem- hcrs.

I n the previous pruhlem. A lamer needc to build a fence from the corner of his ham to the corner of hic chicken house 10 m away in the NE dircction.

Two tughants are maneuvering an w e a n liiw The desired iota1 inrcc i s 3. How long i s the fencc? Two men are trying to pull a crate which will not move y until a lb total force is applied in any one direction.

The N force is to be resolved into components along the AC and AB directions in the xy plane measured by the angles a and p. The orthogonal components of a force are: What IS the sum of the three forces?

The 2. The 1. What force must each man exert to start the box moving as shown? If the component along AC is to be 1. What are the rectangular components of the lb force? Man A can pull only at 45' to the desired direction of crate motion. What is the vector sum of these forces? Y x Figure P.

What is the total cirmpi. What is thc orthogonal total f h x cwnponcnt in tlic. I direction 01 the ioice tiansmittcd to pin A of a roo1 t n h i h i tlic four rncrnher.

What is y? How long mist rncmhel-c OA. What is the unit vector in the direction of the N force'! I 1 where a is the smaller angle between the two vectors. A vector operation that represents such operations con- cisely is the scalar product or dot product. In effect. See the footnote o n p.

The appro- priate sign must. Express the 1. These are unit vectors for cvlindricul coordinates. In other physical problems. Express the unit vectors i. The force lies along diagonal AB. Express the N force in terms of the unit vectors i.

Note that the dot prod- uct may involve vectors of different dimensional representation. I I is 90". Let us next consider the scalar product of mA and n u. How- ever. We can thus conclude that the dot product of equal orthogonal unit vectors for a given reference is unity and that of un- equal orthogonal unit vectors is zero. BJ is independent of the order of multiplication of its terms. The scalar product between unit vectors will now be carried out.

By definition. If we express the vectors A and B in Cartesian components whcn taking the dot product. From the definition. Remember in so doing we must not alter the magnitudcs and directions of the vectors. If we carry it out according to our definitions: If you refer back to Fig. The dot product may be of immediate use in expressing the scalar rec- tangular component of a vector along a given direction as discussed in Sec- tion 2.

Unit vector idirected from 0. If we carry out the dot product of C and s according to our fundamental definition. Example 2. Kvdio transmission tiiwers. What are the length:. How far does the block have to move if the force F is to do I O ft-lb of work? The boat has a velocity component along its axis of 6 kn but because of side slip X and water currents.

If we have for E: A block A is constrained to move along a 20' incline in 2. Explain why the following operations are meaningless: Whenever simply a component is asked for. An electrostatic field E exerts a force on a charged pani- cle of qE. What is cos A. What is the projection of A where I. Given the vectors 2.

A sailboat is tacking into a knot wind. Given the vectors the yz plane. The vector points away from the origin. What are the x and y components of the wind velocity and the boat velocity? What is the angle between the wind d o c - ity and the sailboat velocity'? The force is i n thc diagonal plane GCDE. What is the anglc bctwccn the I. A radio tiiwci is held by guy wires. R to A'! I Fieure P.

What is the angle bctweeii the 1. Whal is thc angle hetween them? Find the dot prtiduct ul the vectors represented hy thz diagonal5 from A to I" arid trmn 1 to G. What is the angle hetween F arid i? The angle a is the smaller of the two angles between the vectors. As in the previous case. The line of action of C is not determined by the cross product.

To set up a convenient operation for these situations. The vector C has an orientation normal to the plane of the vectors A and B. The reader can easily ver- ify this. The sense. We can verify.

The description of vector C is now complete. One such interaction is the moment of a force. Again we remind you that the cross product.

This may he deduced from the nature of the definition. For the two vectors having possibly different dimensions shown in Fig.

If the: It will be left to the student to justil'y the given formulation for each of the vectors in Fig. To do this. Prim using A. Area vzctorc tor prism f i c m Noting that the second and third expressions cancel each olher. We can represent the area of each face of the prism as a vector whose inngnitude equals the area o l the face and whose direction is norm.

The product i X j is unity i n magnitude. Diffcrent kinds of rcfcrcnccs. Since the prism is a closed surface. We then add all six products as follows: It must be cautioned that this method of evaluating a determinant is correct only for 3 x 3 determinants. If the cross product of two vectors involves less than six nonzero components.

To get thc unit normal n I lo plane A B D. S00k ft? Accordingly A I. If the height of the pyramid i s I t. A simple geometric meaning can be associated with this operation. We have set up an xyz reference such that the A and B vectors are in the xy plime. Substituting from Eqs. We see from this example that a plane surface can be represented as a vector.

Thc vector triple product i s a vector quantity and w i l l appear quitc o l t c n i n sttidier oidynamics. A and R in p planc. Using thi. It will he left iis an cxercise Prohleni 2. The projected area then is given as A. The normal n to the infinite plane must have three equal direction cosines. When ire simply identify- ing quantities i n il di. A correct representation o l this Iiirce i n a vector equation would he I. Thus, in Fig.

If the coordinates of vertex E of the inclined pyramid are x A. What is the magnitude of the resulting vector'! What are the cross and dot products for the vectors A and B given as: If vectors A and B in the xy plane have a dot product of SO units, and if the magnitudes of these vectors are I O units and R units, respectively. Y Explain. What is the cross product of the displacement vector from A to B times the displacement vector from C to D'!

I Figure P. In Prvblem 2. Compute the determinant I. Ar Ay A: B, gv B: Compare the result with the computation of A x B C by using the dot-product and crowproduct operations. In Example 2. Give the results in kilo- Figure P.

Check-Oulfor Sections with t 2. What sign iiwst i t hauc'? If so, dcscribc the rcsull. What are the distances that he must travel from Dallas to Topeka and from Topeka ti Chicago'! How long is E the road? See the compass-settings diagram, Fig. Dallas Figure P. Sum all forces acting on the block.

Plane A is parallel to the. We will later m d y the special properties of two par- allel forces called a c o u p k that are opposile in direction atid 2. What is thc cross product between the 1,N force and in magnitude' the diiplaccrnent vector p,,,"'? Four member, of a space frame are loaded as shown.

What are the orthogunill scalar components of the forces on the ball 2. The r and I compunsnti of the force F arc known tu be joint at O? What i q thc f k c F and what are rectangular p;irallelepiped. What are the force components on the electron'? The charge of the electron is l. A skeet shooter is aiming his gun at point A. What is the L. A 2,15,z m 2. For the line segment A X , determine cosines m and n. Using the scalar triple product, find the area projected onto the d a n e N from the surface ABC.

A lh crate is held up by three forces. What Suppose that an electron moves through a uniform magnetic field should forces F , and F, he for this condition'? Important Vector Quantities z. Con- sider first the path of motion of a particle shown dashed in Fig. As indi- cated in Chapter I, the di,splacemenr vecfor p is a directed line segment connecting any two points on the path of motion, such as points I and 2 in Fig.

The displacement vector thus represents the shortest movement of the panicle to get from one position on the path of motion to another. The Figure 3. Displacement vector p purpose of the rectangular parallelepiped shown in the diagram is to convey hetween points 1 and 2.

We can readily express. The directed line segment r from the origin of a coordinate system to a. The notations R and p are also used for position vectors. You can conclude from Chapter 2 that the. The scalar components of a position vector are simply the coordi- Figure 3.

Position vector. To express r in Cartesian components, we then have. Figure 3. Relation hetween a displacement vector and position Yectors. Example 3. YK and XYZ. The position vector o l the origin 0 o l r y: What arc the coor- dinates. From Fig. For Simple Cases.

## Engineering Mechanics

The moment of a force about a point 0 see Fig. And the direction of this vector is perpendicular to the plane of the point and the force, with a sense determined from the familiar right-hand-screw rule. Case B. For Complex Cases. Another apprwach is to employ a position vcctcir r from point 0 to nnypoinf P along the line ol'action of force F as shown Figure 3. The nioment M of F about point 0 will he shown to he given as1.

For the purpose of forming the cross product, the vectors in Fig. Thus, we get the same magnitude of M as with the elementary definition. Also, note that the direction of M here is identical to that of the elementary definition.

Thus we have the same result as for the elementary definition in all pertinent respects. We shall use either of these formulations depending on the situation at hand. Put r from 0 to any point along the line of action of F.

The first of these formulations will he used generally for cases where the force and point are in a convenient plane, and where the perpendicular distance between the point and the line of action of the force is easily mea- sured. As an example, we have shown in Fig. Move vector r end F. Coplanar forces on a beam For a coplanar force system such as this, we may simply give the scalar form of the equation above, as follows: We shall illustrate such a case in Example 3.

Consider next a system of n concurrent forces in Fig. Concurrent forces.

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Wc cim Ihrn s;ly that. As a first step, let us express force F vectorially. Find moments at A and 8. We can then express the force F in the following manner: Xj - A particle mmes along ii circular path in the xy plane.

What poinl 3, 4, 5 ft'! What are its magnitude and direction cosines? What is the displacement vector from position I her position.

What is the distance hetwcen. What is the position vector r for refer-: A particle moves along a paraholic path i n thc i;plane. Find the momcnt of thc SO-lb forcc ahout the support at A din;ilc. Find the moment of the two lorces first ahout point A and hen ahout point R.

I,OOO N 3. An nnillery spotter on Hill rn high eqimiltes the posirioii o i an cncmy tnnk as 3. A nim howmer unil with n range x of I1. Both gun units are located at an elevation -2m, OS Can eillirr o r hoth gun unit, hit thc tank, o r r m w t an air mike be callcd in?

Find the moment of the forces about points A and B. The total equivalent forces from water and gravity are a Use scalar approach. We will soon be able to compute such equiv- b Use vector approach. Compute the mnment of these forces about the toe of the dam in the right-hand comer. It is of plastic material and can rotate so as to be oriented parallel to the flow of water. A uniform friction force distribution from the flow is present on both faces of the flag hav- ing the value of 10 N per square meter.

Also the flagpole has a uniform force from the flow of 20 N per meter of length of the flagpole. Finally there is an upward buoyant force on the flag of Figure P.

What is the moment vector of 3. The crew of a submarine patrol plane, with three-dimen- these forces at the base of the flagpole? Where should the pilot insmct a second patrol plane flying at an elevation of 4. His waist coincides with the pivot of the work capsule.

Three transmission lines are placed unsymmetrically on a power-line pole. For each pole, the weight of a single line when cov- ered with ice is 2,ooO N. What is the moment at the base of a pole? A truck-mounted crane has a m hrxnn inclincd a1 60" to di: A force F from wind, weight. At E there is a ball-and-socket joint which also supports the member. Denoting the forces from the cables as Fer, and FAB. Plane EGD is perpendicular to the wall. Get results in terms of Fro and T,r.

By means of a simple situation, we shall set forth a definition of the moment of a force about an axis. Suppose that a disc I s mounted on a shaft that is free to rotate in a set of bearings, as shown in Fig. A force F, inclined to the plane A of the disc, acts on the disc.

We decompose the force into two coplanar rectangular components, one normal to plane A of the disc and one tangent to plane A of the disc, that is, into forces FB and 5, respectively, so as to form a plane shown tinted, normal to plane A.

You w i l l remember from physics, this product i s nothing more than tlie mmncnt T o compute the moment or tnrque of a force F i n a planc perpendicular to plane A ahout an axis B-B Fig. This plane cuts i3-R a1 I and thc line of action of forcc Fat some poini P. The moment about an a x i s clrarly i s a scalar. The reader will he quick to noLe that Fig.

This latter diagram then takes us back Lo Fig. Accordingly, we note, nn the cine hand. I4la we can get the scalar iiiomciit M ahout an axis B-8 at point n and perpendicular to planc A. Thus, by taking the scalar value o f M in Fig. We can thus conclude, on considering Fig. Consideration of the moment of F about point A. Before continuing, we wish to point out that 4 in Fig.

From Varignon's theorem we can employ these components instead of 6 in computing the moment about the B--B axis. For each force component, we multiply the force times the perpendicular distance from a to the line of action of the force component using the right-hand-screw rule to determine the sense and thus the sign.

When we discussed the moment of a force about apoint, we presented a formulation useful for simple cases i. Thus far, for moments about an axis, we have presented a formulation Fd that is useful for simple cases? For this purpose, we have redrawn Fig. The coordinate distances x, y. The position vector r to P is also shown. The force component FH of Fig. We now compute the moment about the x axis for force F using this new arrangement which does not require F to be in a plane perpendicular to plane A.

Clearly, F, contributes no moment, as before. For Sorce t;. Using the right- hand-scrcw rule fiir: Comparing Eqs. I axis i s simply M ,. We ciin thus concludi: Then draw ii p o s i t h i vector r Iron1 point 0 to any point dong Ihc line 01; d u n of F. Thih h a been shown i n [he diagraiii. We can then hay. Notice from Eqs. Equation 3. The moment of a force about an axis equak the scalar component in the direction qf the axis of the m m e n f vector taken about any point along the axis.

Note that the unit vector n c d n have two opposite senses along the axis n, in contrast to the usual unit vectors i, j, and k associated with the coordinate axes.

Thdt is, a positive moment M,, has a sense corresponding to that of n, and a negative moment M,, has a sense opposite to that o f n. If the opposite sense had been chosen for n, the sign of M n would be opposite to that found in the first case. However, the same physical moment is obtained i n both cases. If we specify the moments of a force about three orthogonal concurrent axes, we then single out one possible point in space for 0 along the axes.

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Point 0,of course. These three moments about orthogonal axes then become the orthogonal scalar components of the moment of I; about point 0, and we can say: The three orthogonal components ojthe moment of a force about a point are the muments of this force about the three o e the point as a n origin. You may now ask what the physical differences are in applications of monients about an axis and moments about a point.

The simplest example is in the dynamics of rigid bodies. If a body is constrained so it can only spin about its axis, as in Fig. The less familiar concept of moment about a point is illustrated in the motion of bod- ies that have n o constrhints, such as missiles and rockets.

In these cases, the rotationiil motion of the body is related by a vector equation to the moment of forces acting on the body about a point called the center ofmass. The center of mass will he defined completely later.

## Prentice Hall, Upper Saddle River, New Jersey

Mathematically, wc have, using a displacement vector from point I tu point u. Find momenl d F ahout line. The formulation ahove i s the s c d a r triple product exani- incd in Chapter 2 and we can usc the determinant approach for the calcu- lation m c e the components 01 the vectors r,, - rl. F , and i j have been determined. I 1 we had chosen p lo have an opposite sense,: Note that the same physical inoinent i s determined in both cases.

The vessel becomes snagged on some rocks and the mother ship steams ahead in a forward direction in an attempt to free the sub- merged vessel. The connecting cable is suspended from a crane directed up over the wdter 20 m above the center of mass of the mother ship and 15 m out from the longitudinal axis of the mother shim The cable transmits a I. It is inclined 50" from the vertical in a vertical plane which. What is the moment tending to cause the mother ship to roll about its longitudi- nal axis ].

What i? Xk k N I What i s the moment ahaut tixis C ' c m the gmund'! What is the momcnt of this force ahout an axis ping through thc paints 6. Compute thc thrurt 01 the applicd tnrcci shown aluog the axis nf the rhair and the torque of the firrcr? What i s the torque of thew blimp i s brces ahout the axis of the shaft'!

What i s the moment of the 3. Disc A has a radius of mm. Q planc md is inclined at 30" from the I axis with a s c n x directed away rom the origin. What is the nioment 01this fircr F about an Figure P. A fmce F acts at position 3. In Problem 3. Find the moment of the I. O n a rigid body.

A couple. The turning action is given quantitatively by the moment of forces about a point or an axis. The ladder weight is 20 kN and is regarded as concen- trated at a point I O m up from the base the lower part of the ladder weighs much more than the upper part. View A-A Figure P.

N fireman and the N young lady he is rescuing are at the top of the lad- der. From the def- inition of thc cross product. Posi- tion vectors have heen drawn in Fig. Points I and 2 may be chosen anywhere along the lines o f action of the forces without changing the resulting moment.

M Figure 3. The sense in this case may he seen in Fig. Let us now evaluate the moment of the couple about thc vrigin. Note also that the riitatiiin of e to F. Since e i s i n thc planc o f the couple. Notc thc use ofthe double arrow to rep- resent the ciiuple miiment. Adding the monient of each force about 0. In short. More about this in the next section.

Since none of these steps changes the direction or magnitude of the couple moment. The particular line of action of the vector representation of the couple moment that is illustrated in Fig. To understand this. Shames is the author of Engineering Mechanics 4. Engineering Mechanics: Statics and Dynamics. Rate this book. Engineering Mechanics has 38 ratings and 1 review. Solid Mechanics. Engineering: Where can I find a free manual solution of Fluid Mechanics by. I do not have any idea about designing and hence the book must cover up the.

This book is designed to provide a mature, in-depth treatment of engineering. The book contains numerous examples, along with their complete solutions. Prentice Hall of India Pvt.Express the dependent quantity dimensionally; substitute existing units for the basic dimensions; and finally, change these units to the equivalent numbers of units in the new system.

A force F, inclined to the plane A of the disc, acts on the disc. Rigid Body. This is illustrated in Fig. A mass M is supported by cables I and 2. There is also an attraction between the two bodies A and B themselves. In effect. YK and XYZ.

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