Pytel and Singer. Solution to Problems in Strength of Materials 4th Edition. Authors: Andrew Pytel and Ferdinand L. Singer. The content of this site is not. , find the values of x and wo so that Strength of Materials (4th Edition) . is Strength of Materials 4th edition by Pytel and Singer Problem A 7/8-in. Problem of text book if the allowable flexural stress is MPa. Strength of Materials, 4th Edition [Solutions Manual] - Singer, Pytel. Course: Material Science (MENG ). Simple Stresses. Simple stresses are expressed as.

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strength of materials by pytel and singer pytel and singer solution to problems in strength of materials 4th edition authors: andrew pytel and ferdinand singer. si te is not endorsed by or affiliated with the author and/or publisher of this book. Strength of Materials [Andrew Pytel, Ferdinand L. Singer] on ruthenpress.info Simplified approach for teaching strength of materials for college student. Hardcover: pages; Publisher: Harpercollins College Div; Subsequent edition (February 1, ) This book is being used as a course book of st. of materials in n.e.d. Strength of Materials 4th Edition by Pytel and Singer - Download as Word Doc . doc), PDF File .pdf), Text File .txt) or read online.

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Equivalent shear force of the plate The resisting area is the shaded area along the perimeter and the shear force is equal to the punching force. Based on shear strength of plate:. Diameter of smallest hole: Based on compression of puncher:. Diameter of the smallest bolt Solution The bolt is subject to double shear.

Shearing stress of the pin at B Solution Width b of the key Solution The smallest diameter pin that can be used at A. The maximum force P that can be applied by the operator Solution Shear area: The axial force P that can be safely applied to the block Solution For safe compressive force, use answer.

Flag for inappropriate content. For Later. Related titles. Strength of Materials 4th Edition by Pytel and Singer. Jump to Page. Search inside document. Force required to punch a mmdiameter hole Solution Required: Maximum thickness of plate: Based on puncher strength: Based on shear strength of plate: Based on compression of puncher: Equivalent shear force for plate Based on shearing of plate: The smallest diameter pin that can be used at A For member BC: Solution For member AB: The maximum force P that can be applied by the operator Solution Equation 2 Based on tension of rod equation 1: Based on shear of rivet equation 2: Shear force: The axial force P that can be safely applied to the block Solution For safe compressive force, use answer Based on maximum compressive stress: Normal force: Muhammad Assim Baig.

Khalid Yousaf. Nath Villena. Ahmad H. Compute the contact pressure and tangential stress in each tube when the aluminum tube is subjected to an internal pressure of 5. Problem In the assembly of the bronze tube and steel bolt shown in Fig. Find the stresses if the nut is given one additional turn.

How many turns of the nut will reduce these stresses to zero? Problem The two vertical rods attached to the light rigid bar in Fig. P are identical except for length. Before the load W was attached, the bar was horizontal and the rods were stress-free.

P is pinned at B and connected to two vertical rods. P, a rigid beam with negligible weight is pinned at one end and attached to two vertical rods. Find the vertical movement of W. Problem As shown in Fig.

P, a rigid bar with negligible mass is pinned at O and attached to two vertical rods. Assuming that the rods were initially tress-free, what maximum load P can be applied without exceeding stresses of MPa in the steel rod and 70 MPa in the bronze rod.

Solution Problem Shown in Fig. P is a section through a balcony. The total uniform load of kN is supported by three rods of the same area and material. Compute the load in each rod. Assume the floor to be rigid, but note that it does not necessarily remain horizontal. Solution Problem Three rods, each of area mm2, jointly support a 7.

Assuming that there was no slack or stress in the rods before the load was applied, find the stress in each rod. Initially, the assembly is stressfree. Horizontal movement of the joint at A is prevented by a short horizontal strut AE.

Thermal Stress Temperature changes cause the body to expand or contract. If temperature deformation is permitted to occur freely, no load or stress will be induced in the structure. In some cases where temperature deformation is not permitted, an internal stress is created.

The internal stress created is termed as thermal stress. For a homogeneous rod mounted between unyielding supports as shown, the thermal stress is computed as: If the wall yields a distance of x as shown, the following calculations will be made: Take note that as the temperature rises above the normal, the rod will be in compression, and if the temperature drops below the normal, the rod is in tension.

At what temperature will the stress be zero? At what temperature will the rails just touch? What stress would be induced in the rails at that temperature if there were no initial clearance?

Solution Problem A steel rod 3 feet long with a cross-sectional area of 0. Solution Problem A bronze bar 3 m long with a cross sectional area of mm2 is placed between two rigid walls as shown in Fig.

Find the temperature at which the compressive stress in the bar will be 35 MPa. Problem Calculate the increase in stress for each segment of the compound bar shown in Fig. Assume that the supports are unyielding and that the bar is suitably braced against buckling.

Neglect the deformation of the wheel caused by the pressure of the tire. P is pinned at B and attached to the two vertical rods. Initially, the bar is horizontal and the vertical rods are stress-free. Neglect the weight of bar ABC.

P, there is a gap between the aluminum bar and the rigid slab that is supported by two copper bars. Problem A bronze sleeve is slipped over a steel bolt and held in place by a nut that is turned to produce an initial stress of psi in the bronze. Problem A rigid bar of negligible weight is supported as shown in Fig.

Assume the coefficients of linear expansion are Solution Problem For the assembly in Fig. Problem The composite bar shown in Fig. Figure P and P Solution Problem At what temperature will the aluminum and steel segments in Prob. Problem A rigid horizontal bar of negligible mass is connected to two rods as shown in Fig. If the system is initially stress-free. Calculate the temperature change that will cause a tensile stress of 90 MPa in the brass rod. Assume that both rods are subjected to the change in temperature.

Solution Problem Four steel bars jointly support a mass of 15 Mg as shown in Fig.

Each bar has a cross-sectional area of mm2. Such a bar is said to be in torsion. For solid cylindrical shaft: For hollow cylindrical shaft: Solved Problems in Torsion Problem A steel shaft 3 ft long that has a diameter of 4 in.

Determine the maximum shearing stress and the angle of twist. What maximum shearing stress is developed? Solution Problem A steel marine propeller shaft 14 in. What power can be transmitted by the shaft at 20 Hz? Solution Problem A 2-in-diameter steel shaft rotates at rpm. If the shearing stress is limited to 12 ksi, determine the maximum horsepower that can be transmitted. Problem A steel propeller shaft is to transmit 4. Solution Problem An aluminum shaft with a constant diameter of 50 mm is loaded by torques applied to gears attached to it as shown in Fig.

Solution Problem A flexible shaft consists of a 0. Determine the maximum length of the shaft if the shearing stress is not to exceed 20 ksi. What will be the angular deformation of one end relative to the other end? Problem Determine the maximum torque that can be applied to a hollow circular steel shaft of mm outside diameter and an mm inside diameter without exceeding a shearing stress of 60 MPa or a twist of 0. Solution Problem The steel shaft shown in Fig.

Solution Problem A 5-m steel shaft rotating at 2 Hz has 70 kW applied at a gear that is 2 m from the left end where 20 kW are removed. At the right end, 30 kW are removed and another 20 kW leaves the shaft at 1. Problem A compound shaft consisting of a steel segment and an aluminum segment is acted upon by two torques as shown in Fig.

Determine the maximum permissible value of T subject to the following conditions: Solution Problem A hollow bronze shaft of 3 in. The two shafts are then fastened rigidly together at their ends.

What torque can be applied to the composite shaft without exceeding a shearing stress of psi in the bronze or 12 ksi in the steel? Problem A solid aluminum shaft 2 in. Determine the maximum shearing stress in each segment and the angle of rotation of the free end.

Solution Problem The compound shaft shown in Fig. P is attached to rigid supports. Problem In Prob. What torque T is required? Solution Problem A torque T is applied, as shown in Fig.

P, to a solid shaft with built-in ends. How would these values be changed if the shaft were hollow? Solution Problem A solid steel shaft is loaded as shown in Fig. Determine the maximum shearing stress developed in each segment. Problem The compound shaft shown in Fig. For the bronze segment AB, the maximum shearing stress is limited to psi and for the steel segment BC, it is limited to 12 ksi.

Problem The two steel shaft shown in Fig. P, each with one end built into a rigid support have flanges rigidly attached to their free ends. The shafts are to be bolted together at their flanges. Determine the maximum shearing stress in each shaft after the shafts are bolted together.

Flanged Bolt Couplings In shaft connection called flanged bolt couplings see figure above , the torque is transmitted by the shearing force P created in he bolts that is assumed to be uniformly distributed.

For any number of bolts n, the torque capacity of the coupling is If a coupling has two concentric rows of bolts, the torque capacity is where the subscript 1 refer to bolts on the outer circle an subscript 2 refer to bolts on the inner circle.

See figure. For rigid flanges, the shear deformations in the bolts are proportional to their radial distances from the shaft axis. Solved Problems in Flanged Bolt Couplings Problem A flanged bolt coupling consists of ten mmdiameter bolts spaced evenly around a bolt circle mm in diameter. Determine the torque capacity of the coupling if the allowable shearing stress in the bolts is 40 MPa. Determine the torque capacity of the coupling if the allowable shearing stress in the bolts is psi.

Solution Problem A flanged bolt coupling consists of eight mmdiameter steel bolts on a bolt circle mm in diameter, and six mm- diameter steel bolts on a concentric bolt circle mm in diameter, as shown in Fig.

What torque can be applied without exceeding a shearing stress of 60 MPa in the bolts?

Determine the shearing stress in the bolts. Problem Determine the number of mm-diameter steel bolts that must be used on the mm bolt circle of the coupling described in Prob. What torque can be applied without exceeding psi in the steel or psi in the aluminum?

Solution Problem A plate is fastened to a fixed member by four mm diameter rivets arranged as shown in Fig. Compute the maximum and minimum shearing stress developed. P to the fixed member.

Using the results of Prob. What additional loads P can be applied before the shearing stress in any rivet exceeds psi? Problem The plate shown in Fig. P is fastened to the fixed member by five mm-diameter rivets. Compute the value of the loads P so that the average shearing stress in any rivet does not exceed 70 MPa. Determine the wall thickness t so as not to exceed a shear stress of 80 MPa. What is the shear stress in the short sides? Neglect stress concentration at the corners. Problem A tube 0.

What torque will cause a shearing stress of psi? Determine the smallest permissi g. Solution Problem A tube 2 mm thick has the shape shown in Fig. Assume that the shearing stress at any point is proportional to its radial distance. Helical Springs When close-coiled helical spring, composed of a wire of round rod of diameter d wound into a helix of mean radius R with n number of turns, is subjected to an axial load P produces the following stresses and elongation: 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. Problem Determine the maximum shearing stress and elongation in a bronze helical spring composed of 20 turns of 1.

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 distance of x from he left support and the portion of the beam to the right of C be removed. 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 ind C a icated 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. Problem Cantilever beam loaded as shown in Fig. Problem Cantilever beam carrying the uniformly varying load shown in Fig. Problem Cantilever beam carrying a distributed load with intensity varying from wo at the free end to zero at the wall, as shown in Fig. Problem Cantilever beam carrying the load shown in Fig.

Problem Beam carrying uniformly varying load shown in Fig. Problem Beam carrying the triangular loading shown in Fig. Solution Problem Beam loaded as shown in Fig.

Problem A total distributed load of 30 kips supported by a uniformly distributed reaction as shown in Fig. Problem Write the shear and moment equations for the semicircular arch 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.

Problem Cantilever beam acted upon by a uniformly distributed load and a couple as shown in Fig. Problem Beam loaded as shown in P Problem Overhang beam loaded by a force and a couple as shown in Fig.

Problem Beam loaded and supported as shown in Fig. Problem A distributed load is supported by two distributedreactions as shown in Fig.

P Solution Problem The beam loaded as shown in Fig. P consists of two segments joined by a frictionless hinge at which the bending moment is zero. Problem A beam supported on three reactions as shown in Fig. 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 , which act at the ends of the vertical membersshown in Fig.

P- 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. Problem Beam carrying the uniformly varying load shown in Fig. Problem Beam carrying the triangular loads shown in Fig.

Problem Beam carrying the loads shown in Fig. Specify values at all change of load positions and at all points of zero shear. Problem Shear diagram as shown in Fig. Moving Loads From the previous section, we see that the maximum moment occurs at a point of zero shears.

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. 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. Problem Repeat Prob. Problem A tractor weighing lb, with a wheel base of 9 ft, carries lb of its load on the rear wheels.

Compute the maximum moment and maximum shear when crossing a 14 ft-span. Problem Three wheel loads roll as a unit across a ft span. Determine the maximum moment and maximum shear in the simply supported span. Problem A truck and trailer combination crossing a m span has axle loads of 10, 20, and 30 kN separated respectively by distances of 3 and 5 m.

Compute the maximum moment and maximum shear developed in the span. Stresses in Beams Forces and couples acting on the beam cause bending flexural stresses and shearing stresses on any cross section of the beam and deflection perpendicular to the longitudinal axis of the beam.

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 beam curvature is: 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. Problem A simply supported beam, 2 in wide by 4 in high and 12 ft long is subjected to a concentrated load of lb at a point 3 ft from one of the supports. Determine the maximum fiber stress and the stress in a fiber located 0.

Problem A high strength steel band saw, 20 mm wide by 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. Problem In a laboratory test of a beam loaded by end couples, the fibers at layer AB in Fig. Problem Determine the minimum height h of the beam shown in Fig. 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? Problem The circular bar 1 inch in diameter shown in Fig. 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.

Problem The right-angled frame shown in Fig. 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. Problem A ft beam, simply supported at 6 ft from either end carries a uniformly distributed load of intensity wo over its entire length. 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. Problem A box beam is composed of four planks, each 2 inches by 8 inches, securely spiked together to form the section shown in Fig.

Determine W if the flexural stress is limited to MPa. Problem A square timber beam used as a railroad tie is supported by a uniformly distributed loads and carries two uniformly distributed loads each totaling 48 kN as shown in Fig.

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? Problem A ft beam simply supported at the ends carries a concentrated load of lb at midspan. 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.

Floor Framing In floor framing, the subfloor is supported by light beams called floor joists or simply joists which in turn supported by heavier beams called girders then girders pass the load to columns. 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. Problem Timbers 12 inches by 12 inches, spaced 3 feet apart on centers, are driven into the ground and act as cantilever beams to back-up the sheet piling of a coffer dam.

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 Problem The ft long floor beams in a building are simply supported at their ends and carry a floor load of 0. Problem Select the lightest W shape sections that can be used for the beams and girders in Illustrative Problem of text book if the allowable flexural stress is MPa.