Strength of materials by singer solution manual pdf download

This book deals with the whole topic covering the mechanics of different materials that are being used extensively in building. You may need to learn the Civil Engineering Calculations Manual solution. This area of research explores how much pressure a substance can withstand without cracking or deforming.

Each day various forces operate on a material and the best option is a material that can withstand these for the longest period of time without failure. This pressure produces a mechanical, internal force. The authors based on various methods which are used to see how much stress a material can bear. Everything in Mechanics of Materials solution is written in this text in a comprehensive manner, so that students quickly and easily understand different factors.

The latest version of Strength of Materials 4th Ed. It has updated material, and exercises to support the readers are also included. Reviews for fast learning revision exist in Strength of Materials 4th Ed. The reference appendix also lets you find out just what you need. The book will also inform you about the calculation about engineering. Thanks for being with us. Next article Why is the head of the pile broken for Pile Cut off Level?

Mechanics of Materials 8th Edition by R. Comment: Please enter your comment! Most Popular. Load more. Solution Problem As shown in Fig. If each rod has a crosssectional area of 0. If w is the weight per unit volume, find the elongation of the rod caused by its own weight. Use this result to determine the elongation of a cone suspended from its base.

The gage length was 50 mm. Plot the stress-strain diagram and determine the following mechanical properties: a proportional limits; b modulus of elasticity; c yield point; d ultimate strength; and e rupture strength. Solution Problem The following data were obtained during a tension test of an aluminum alloy. The initial diameter of the test specimen was 0. Plot the stress-strain diagram and determine the following mechanical properties: a proportional limit; b modulus of elasticity; c yield point; d yield strength at 0.

An element subject to shear does not change in length but undergoes a change in shape. The relationship between the shearing deformation and the applied shearing force is where V is the shearing force acting over an area As.

Poisson's Ratio When a bar is subjected to a tensile loading there is an increase in length of the bar in the direction of the applied load, but there is also a decrease in a lateral dimension perpendicular to the load. For most steel, it lies in the range of 0. Compressive stresses and contraction are taken as negative. The block is subjected to a triaxial loading of three uniformly distributed forces as follows: 48 kips tension in the x direction, 60 kips compression in the y direction, and 54 kips tension in the z direction.

Solution Problem A welded steel cylindrical drum made of a mm plate has an internal diameter of 1. Compute the change in diameter that would be caused by an internal pressure of 1. Assume that Poisson's ratio is 0. Solution Problem A 2-in. Find the tangential stress if an axial compressive load of lb is applied. It fits without clearance in an mm hole in a rigid block. The tube is then subjected to an internal pressure of 4.

Solution Problem A 6-in. With no internal pressure, the tube just fits between two rigid end walls. Calculate the longitudinal and tangential stresses for an internal pressure of psi. These cases require the use of additional relations that depend on the elastic deformations in the members. Solved Problems in Statically Indeterminate Members Problem A steel bar 50 mm in diameter and 2 m long is surrounded by a shell of a cast iron 5 mm thick. Compute the load that will compress the combined bar a total of 0.

Determine the required area of the reinforcing steel if the allowable stresses are 6 MPa and MPa for the concrete and steel, respectively. Solution Problem A timber column, 8 in. Determine the thickness t so that the column will support an axial load of kips without exceeding a maximum timber stress of psi or a maximum steel stress of 20 ksi. The moduli of elasticity are 1. Solution Problem A rigid block of mass M is supported by three symmetrically spaced rods as shown in fig P Determine the largest mass M which can be supported.

Solution Problem The lower ends of the three bars in Fig. P are at the same level before the uniform rigid block weighing 40 kips is attached. Each steel bar has a length of 3 ft, and area of 1. For the bronze bar, the area is 1. Determine a the length of the bronze bar so that the load on each steel bar is twice the load on the bronze bar, and b the length of the bronze that will make the steel stress twice the bronze stress. Solution Problem The rigid platform in Fig.

P has negligible mass and rests on two steel bars, each The center bar is aluminum and Solution Problem Three steel eye-bars, each 4 in.

The center-line spacing between the holes is 30 ft in the two outer bars, but 0. Find the shearing stress developed in the drip pins. Neglect local deformation at the holes. P, three steel wires, each 0. Their unstressed lengths are P consists of a light rigid bar AB, pinned at O, that is attached to the steel and aluminum rods.

Compute the stress in the aluminum rod when the lower end of the steel rod is attached to its support. It carries an axial load P applied as shown in Fig. Determine the stress in segment BC. Hint: Use the results of Prob.

Then use the principle of superposition to compute the reactions when both loads are applied. P is firmly attached to unyielding supports. Solution Problem The composite bar in Fig. P is stress-free before the axial loads P1 and P2 are applied. Solution Problem There is a radial clearance of 0.

The inside diameter of the aluminum tube is mm, and the wall thickness of each tube is 2. Compute the contact pressure and tangential stress in each tube when the aluminum tube is subjected to an internal pressure of 5. Find the stresses if the nut is given one additional turn. How many turns of the nut will reduce these stresses to zero? 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. 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. 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. 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. 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. Assume the coefficients of linear expansion are Solution Problem For the assembly 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. 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.

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? 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.

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?

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. 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. 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.

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. 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. 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. 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? 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. What torque will cause a shearing stress of psi? Determine the smallest permissible dimension a if the shearing stress is limited to psi.

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. 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: A. 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. 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.

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.