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Stress is the lead to accurately describe and predict the elastic deformation of a body. Simple stress can be classified as normal stress, shear stress, and bearing stress. Normal stress develops when a force is applied perpendicular to the cross-sectional area of the material. If the force is going to pull the material, the stress is said to be tensile stress and compressive stress develops when the material is being compressed by two opposing forces.

Shear stress is developed if the applied force is parallel to the resisting area. Example is the bolt that holds the tension rod in its anchor.

Another condition of shearing is when we twist a bar along its longitudinal axis. This type of shearing is called torsion and covered in Chapter 3. Another type of simple stress is the bearing stress, it is the contact pressure between two bodies.

Suspension bridges are good example of structures that carry these stresses. The weight of the vehicle is carried by the bridge deck and passes the force to the stringers vertical cables , which in turn, supported by the main suspension cables. The suspension cables then transferred the force into bridge towers.

Normal Stress Stress Stress is the expression of force applied to a unit area of surface. Another unit of stress which is not commonly used is the dynes cgs unit. Stress is the ratio of force over area.

Simple Stresses There are three types of simple stress namely; normal stress, shearing stress, and bearing stress. Normal Stress The resisting area is perpendicular to the applied force, thus normal. There are two types of normal stresses; tensile stress and compressive stress. Tensile stress applied to bar tends the bar to elongate while compressive stress tend to shorten the bar. The maximum stress in tension or compression occurs over a section normal to the load.

Problem A homogeneous kg bar AB is supported at either end by a cable as shown in Fig. Calculate the smallest area of each cable if the stress is not to exceed 90 MPa in bronze and MPa in steel. Figure P Problem The homogeneous bar shown in Fig. P is supported by a smooth pin at C and a cable that runs from A to B around the smooth peg at D. Find the stress in the cable if its diameter is 0. Problem A rod is composed of an aluminum section rigidly attached between steel and bronze sections, as shown in Fig.

Axial loads are applied at the positions indicated. Problem An aluminum rod is rigidly attached between a steel rod and a bronze rod as shown in Fig. Problem Determine the largest weight W that can be supported by two wires shown in Fig.

The stress in either wire is not to exceed 30 ksi. The cross-sectional areas of wires AB and AC are 0. Problem A inches square steel bearing plate lies between an 8-inches diameter wooden post and a concrete footing as shown in Fig. Determine the maximum value of the load P if the stress in wood is limited to psi and that in concrete to psi. Problem For the truss shown in Fig. The crosssectional area of each member is 1.

Indicate tension T or compression C. P above. The stresses are not to exceed 20 ksi in tension and 14 ksi in compression. A reduced stress in compression is specified to reduce the danger of buckling. Indicate the tension or compression. The cross sectional area of each member is mm2. P is supported by a cable that runs from A to B around the smooth peg at E, a vertical cable at C, and a smooth inclined surface at D.

Determine the mass of the heaviest bar that can be supported if the stress in each cable is limited to MPa. The area of the cable AB is mm2 and that of the cable at C is mm2. Shearing Stress Forces parallel to the area resisting the force cause shearing stress. It differs to tensile and compressive stresses, which are caused by forces perpendicular to the area on which they act.

Shearing stress is also known as tangential stress. Solution Problem As in Fig. The compressive stress in the punch is limited to 50 ksi.

Problem Find the smallest diameter bolt that can be used in the clevis shown in Fig. The shearing strength of the bolt is MPa. Problem A mm-diameter pulley is prevented from rotating relative to mm-diameter shaft by a mm-long key, as shown in Fig. Problem Compute the shearing stress in the pin at B for the member supported as shown in Fig. The pin diameter is 20 mm. Problem The members of the structure in Fig. Determine the smallest diameter pin that can be used at A if the shearing stress is limited to psi.

Assume single shear. Problem Referring to Fig. P, compute the maximum force P that can be applied by the machine operator, if the shearing stress in the pin at B and the axial stress in the control rod at C are limited to psi and psi, respectively. The diameters are 0. Assume single shear for the pin at B. Using the free-body diagram concept in Fig. Problem A rectangular piece of wood, 50 mm by mm in cross section, is used as a compression block shown in Fig.

Hint: Use the results in Problem Bearing Stress Bearing stress is the contact pressure between the separate bodies. It differs from compressive stress, as it is an internal stress caused by compressive forces. The allowable stresses are MPa for bearing in the plate material and 60 MPa for shearing of rivet. Determine a the minimum thickness of each plate; and b the largest average tensile stress in the plates. Problem The lap joint shown in Fig. Calculate the maximum safe load P that can be applied if the shearing stress in the rivets is limited to 14 ksi and the bearing stress in the plates is limited to 18 ksi.

Assume the applied load is uniformly distributed among the four rivets. Problem In the clevis shown in Fig. Find the allowable load on the connection. The nut is tightened to cause a tensile stress of 18 ksi in the bolt. Compute the shearing stress in the head of the bolt and in the threads. Problem Figure P shows a roof truss and the detail of the riveted connection at joint B. Member BE? What is the largest average tensile or compressive stress in BC and BE?

Problem Repeat Problem if the rivet diameter is 22 mm and all other data remain unchanged. Thin-Walled Pressure Vessels A tank or pipe carrying a fluid or gas under a pressure is subjected to tensile forces, which resist bursting, developed across longitudinal and transverse sections.

The length of the tank is L and the wall thickness is t. Isolating the right half of the tank:. If there exist an external pressure po and an internal pressure pi, the formula may be expressed as:. It can be observed that the tangential stress is twice that of the longitudinal stress.

Calculate the allowable internal pressure if the stress is limited to psi. Problem Calculate the minimum wall thickness for a cylindrical vessel that is to carry a gas at a pressure of psi. The diameter of the vessel is 2 ft, and the stress is limited to 12 ksi. Problem A cylindrical pressure vessel is fabricated from steel plating that has a thickness of 20 mm.

The diameter of the pressure vessel is mm and its length is 2. Determine the maximum internal pressure that can be applied if the longitudinal stress is limited to MPa, and the circumferential stress is limited to 60 MPa. Find the maximum height to which the tank may be filled if the circumferential stress is limited to psi. The specific weight of water is Problem The strength of longitudinal joint in Fig.

Calculate the maximum diameter of the cylinder tank if the internal pressure is psi. At what revolutions per minute rpm will the stress reach 30 ksi if the mean radius is 10 in.? Problem At what angular velocity will the stress of the rotating steel ring equal MPa if its mean radius is mm?

The density of steel 7.

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## Solucionario Resistencia De Materiales Ferdinand L. Singer, Andrew Pytel 4 Edicion

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