Using the free-body diagram concept in Fig. a Solution Note: Textbook is Strength of Materials 4th edition by Pytel and Singer Problem A 7/8-in. DOWNLOAD – Strength Of Materials Book (PDF) By hackbus.info And hackbus.info – Free Download PDF. Strength Of Materials Standard Books – PDF Free Download Strength Of Materials Standard STRENGTH OF MATERIALS BY hackbus.info AND A. PYTEL.
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Browse and Download Strength of Materials books of various titles, written by many authors and Download eBooks for free from Engineering study Material site. Strength of materials by singer and pytel (4th edt). 11, views. Share; Like; Download Abdullah Al Naser., Coordinator. Follow. Published. Strength of Materials 4th Edition by Pytel and Singer. Given: Weight of Consider the free body diagram in the transverse section of the tank: The total force.
Assume that the shearing stress at any point is proportional to its radial distance. This formula neglects the curvature of the spring. For heavy springs and considering the curvature of the spring, a more precise formula is given by: Use Eq. Compute the number of turns required to permit an elongation of 4 in. Solution Problem Compute the maximum shearing stress developed in a phosphor bronze spring having mean diameter of mm and consisting of 24 turns of mm-diameter wire when the spring is stretched mm.
Solution Problem Two steel springs arranged in series as shown in Fig. P supports a load P. The upper spring has 12 turns of mm-diameter wire on a mean radius of mm. The lower spring consists of 10 turns of mmdiameter wire on a mean radius of 75 mm. If the maximum shearing stress in either spring must not exceed MPa, compute the maximum value of P and the total elongation of the assembly.
Compute the equivalent spring constant by dividing the load by the total elongation. Solution Problem A rigid bar, pinned at O, is supported by two identical springs as shown in Fig.
Determine the maximum load W that may be supported if the shearing stress in the springs is limited to 20 ksi. Solution Problem A rigid bar, hinged at one end, is supported by two identical springs as shown in Fig. Each spring consists of 20 turns of mm wire having a mean diameter of mm.
Compute the maximum shearing stress in the springs, using Eq. Neglect the mass of the rigid bar. P, a homogeneous kg rigid block is suspended by the three springs whose lower ends were originally at the same level. Compute the maximum shearing stress in each spring using Eq. According to determinacy, a beam may be determinate or indeterminate. The beams shown below are examples of statically determinate beams. In order to solve the reactions of the beam, the static equations must be supplemented by equations based upon the elastic deformations of the beam.
The degree of indeterminacy is taken as the difference between the umber of reactions to the number of equations in static equilibrium that can be applied.
These loads are shown in the following figures. Assume that the beam is cut at point C a distance of x from he left support and the portion of the beam to the right of C be removed.
Strength of Materials: Andrew Pytel, Ferdinand L. Singer: hackbus.info: Books
The portion removed must then be replaced by vertical shearing force V together with a couple M to hold the left portion of the bar in equilibrium under the action of R1 and wx. The couple M is called the resisting moment or moment and the force V is called the resisting shear or shear. The sign of V and M are taken to be positive if they have the senses indicated above. In each problem, let x be the distance measured from left end of the beam.
Also, draw shear and moment diagrams, specifying values at all change of loading positions and at points of zero shear.
Neglect the mass of the beam in each problem. Problem Beam loaded as shown in Fig. Solution Problem Beam loaded as shown in Fig.
P if a the load P is vertical as shown, and b the load is applied horizontally to the left at the top of the arch. Differentiate V with respect to x gives Thus, the rate of change of the shearing force with respect to x is equal to the load or the slope of the shear diagram at a given point equals the load at that point.
The area of the shear diagram to the left or to the right of the section is equal to the moment at that section. The slope of the moment diagram at a given point is the shear at that point. The slope of the shear diagram at a given point equals the load at that point. The maximum moment occurs at the point of zero shears. This is in reference to property number 2, that when the shear also the slope of the moment diagram is zero, the tangent drawn to the moment diagram is horizontal.
When the shear diagram is increasing, the moment diagram is concave upward. When the shear diagram is decreasing, the moment diagram is concave downward. A force that tends to bend the beam downward is said to produce a positive bending moment. A force that tends to shear the left portion of the beam upward with respect to the right portion is said to produce a positive shearing force.
An easier way of determining the sign of the bending moment at any section is that upward forces always cause positive bending moments regardless of whether they act to the left or to the right of the exploratory section.
Give numerical values at all change of loading positions and at all points of zero shear. Note to instructor: Problems to may also be assigned for solution by semi graphical method describes in this article. P consists of two segments joined by a frictionless hinge at which the bending moment is zero. P consists of two segments joined by frictionless hinge at which the bending moment is zero. Draw shear and moment diagrams for each of the three parts of the frame. It is subjected to the loads shown in Fig.
P, which act at the ends of the vertical members BE and CF. These vertical members are rigidly attached to the beam at B and C. Draw shear and moment diagrams for the beam ABCD only. Specify values at all change of load positions and at all points of zero shear.
Problem Shear diagram as shown in Fig.
For beams loaded with concentrated loads, the point of zero shears usually occurs under a concentrated load and so the maximum moment. Beams and girders such as in a bridge or an overhead crane are subject to moving concentrated loads, which are at fixed distance with each other.
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The problem here is to determine the moment under each load when each load is in a position to cause a maximum moment. The largest value of these moments governs the design of the beam. With this rule, we compute the maximum moment under each load, and use the biggest of the moments for the design.
Usually, the biggest of these moments occurs under the biggest load. The maximum shear occurs at the reaction where the resultant load is nearest. Usually, it happens if the biggest load is over that support and as many a possible of the remaining loads are still on the span. In determining the largest moment and shear, it is sometimes necessary to check the condition when the bigger loads are on the span and the rest of the smaller loads are outside. Solved Problems in Moving Loads Problem A truck with axle loads of 40 kN and 60 kN on a wheel base of 5 m rolls across a m span.
Compute the maximum bending moment and the maximum shearing force. Compute the maximum moment and maximum shear when crossing a 14 ft-span. Determine the maximum moment and maximum shear in the simply supported span. Compute the maximum moment and maximum shear developed in the span. If couples are applied to the ends of the beam and no forces act on it, the bending is said to be pure bending. If forces produce the bending, the bending is called ordinary bending.
Flexure Formula Stresses caused by the bending moment are known as flexural or bending stresses. Consider a beam to be loaded as shown. Since the curvature of the beam is very small, bcd and Oba are considered as similar triangles. Considering a differential area dA at a distance y from N. The maximum bending stress may then be written as This form is convenient because the values of S are available in handbooks for a wide range of standard structural shapes.
Determine the maximum fiber stress and the stress in a fiber located 0. What maximum flexural stress is developed? What minimum diameter pulleys can be used without exceeding a flexural stress of MPa? Compute the stress in the bar and the magnitude of the couples. P if the flexural stress is not to exceed 20 MPa. Solution Problem A section used in aircraft is constructed of tubes connected by thin webs as shown in Fig. Each tube has a cross-sectional area of 0. If the average stress in the tubes is no to exceed 10 ksi, determine the total uniformly distributed load that can be supported in a simple span 12 ft long.
Neglect the effect of the webs. Solution Problem A mm diameter bar is used as a simply supported beam 3 m long.
Determine the largest uniformly distributed load that can be applied over the right two-thirds of the beam if the flexural stress is limited to 50 MPa. What is the maximum length of the beam if the flexural stress is limited to psi?
P is bent into a semicircle with a mean radius of 2 ft. Neglect the deformation of the bar. Solution Problem A rectangular steel beam, 2 in wide by 3 in deep, is loaded as shown in Fig. Determine the magnitude and the location of the maximum flexural stress. P carries a uniformly distributed loading equivalent to N for each horizontal projected meter of the frame; that is, the total load is N.
Compute the maximum flexural stress at section a-a if the cross-section is 50 mm square. Solution Problem A timber beam AB, 6 in wide by 10 in deep and 10 ft long, is supported by a guy wire AC in the position shown in Fig.
The beam carries a load, including its own weight, of lb for each foot of its length. Compute the maximum flexural stress at the middle of the beam. Solution Problem A rectangular steel bar, 15 mm wide by 30 mm high and 6 m long, is simply supported at its ends. What uniformly distributed load can be carried, in addition to the weight of the beam, without exceeding a flexural stress of MPa if a the webs are vertical and b the webs are horizontal?
Refer to Appendix B of text book for channel properties. Calculate the maximum value of wo if the flexural stress is limited to 20 ksi. Be sure to include the weight of the beam. Find the maximum uniformly distributed load that can be applied over the entire length of the beam, in addition to the weight of the beam, if the flexural stress is not to exceed MPa.
Compute the maximum length of the beam if the flexural stress is not to exceed 20 ksi. Determine W if the flexural stress is limited to MPa. Determine the size of the section if the maximum stress is limited to 8 MPa. Solution Problem A wood beam 6 in wide by 12 in deep is loaded as shown in Fig.
If the maximum flexural stress is psi, find the maximum values of wo and P which can be applied simultaneously? This means that for a rectangular or circular section a large portion of the cross section near the middle section is understressed. For steel beams or composite beams, instead of adopting the rectangular shape, the area may be arranged so as to give more area on the outer fiber and maintaining the same overall depth, and saving a lot of weight.
When using a wide flange or I-beam section for long beams, the compression flanges tend to buckle horizontally sidewise. This buckling is a column effect, which may be prevented by providing lateral support such as a floor system so that the full allowable stresses may be used, otherwise the stress should be reduced.
The reduction of stresses for these beams will be discussed in steel design.
In selecting a structural section to be used as a beam, the resisting moment must be equal or greater than the applied bending moment.
The equation above indicates that the required section modulus of the beam must be equal or greater than the ratio of bending moment to the maximum allowable stress. A check that includes the weight of the selected beam is necessary to complete the calculation. In checking, the beams resisting moment must be equal or greater than the sum of the live-load moment caused by the applied loads and the dead-load moment caused by dead weight of the beam.
Dividing both sides of the above equation by fb max, we obtain the checking equation Assume that the beams in the following problems are properly braced against lateral deflection. Be sure to include the weight of the beam itself. What is the lightest W shape beam that will not exceed a flexural stress of MPa? What is the actual maximum stress in the beam selected? Select the lightest S section that can be employed using an allowable stress of 18 ksi. Select the lightest S section that can be used if the allowable stress is 20 ksi.
Using an allowable stress of 20 ksi, determine the lightest suitable W shape beam. What is the actual maximum stress in the selected beam? If the allowable stress is 18 ksi, select the lightest suitable W shape. If the allowable stress is MPa, determine the lightest W shape beam that can be used. Compute the center-line spacing between joists to develop a bending stress of 8 MPa. What safe floor load could be carried on a center-line spacing of 0. Solution Problem Timbers 8 inches wide by 12 inches deep and 15 feet long, supported at top and bottom, back up a dam restraining water 9 feet deep.
Water weighs Neglect the weights of the members. The total loading including live and dead loads in each bay is as shown. Select the lightest suitable W if the allowable flexural stress is MPa. Thus for a symmetrical section such as wide flange, the compressive and tensile stresses will be the same. This will be desirable if the material is both equally strong in tension and compression.
However, there are materials, such as cast iron, which are strong in compression than in tension. It is therefore desirable to use a beam with unsymmetrical cross section giving more area in the compression part making the stronger fiber located at a greater distance from the neutral axis than the weaker fiber.
Some of these sections are shown below.
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The proportioning of these sections is such that the ratio of the distance of the neutral axis from the outermost fibers in tension and in compression is the same as the ratio of the allowable stresses in tension and in compression. Thus, the allowable stresses are reached simultaneously. In this section, the following notation will be use: The beam carries a uniformly distributed load of intensity wo over its entire length. Determine the maximum safe value of P if the working stresses are 4 ksi in tension and 10 ksi in compression.
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Actions Shares. Embeds 0 No embeds. No notes for slide. Strength of materials by singer and pytel 4th edt 1. I 1 -'-: E- r'! F; aaz ;: El li': Ea- ai,: L 2 iii7 l;9 i. Zii X: E ii ,tzt;i: B ,ii: L Eil;iii: E;ii,'- ; -1": Strength of Materials Dover Books on Physics. Den Hartog. Read more. Product details Hardcover: English ISBN Tell the Publisher! I'd like to read this book on Kindle Don't have a Kindle? Share your thoughts with other customers.
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The fit is OK but the material is sensitive to static electricity You can see the thing sparkling as you pick it up and open it in preparation to putting it on. Can not recommend it. This book is being used as a course book of st. Ihope my review would be given due consideration.
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