Lecture mechanics of materials chapter ten design and failure
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Lecture mechanics of materials chapter ten design and failure
M. VtbkMwhaiilcs of Materials: Design and FailureIV I ■*?!CHAPTER TENDESIGN AND FAILURELearning objectives1.Learn the computation of stresses and stra Lecture mechanics of materials chapter ten design and failure ains on a stmctiual member under combined axial, torsion, and bending loads.2.Develop the design and analysis skills for structures constructed from one-dimensional members.In countless engineering applications, the structural members arc subjected a combination of loads The propeller on a boat (Fig Lecture mechanics of materials chapter ten design and failure ure 10 Id) subjects the shaft to an axial force as it pushes the water backward, but also a torsional load as It hints through the water. Gravity subjLecture mechanics of materials chapter ten design and failure
ects the Washington Monument (Figure 10.1 b) to a distributed axial load, while the wind pressure of a storm subjects the monument to bending loads. IM. VtbkMwhaiilcs of Materials: Design and FailureIV I ■*?!CHAPTER TENDESIGN AND FAILURELearning objectives1.Learn the computation of stresses and stra Lecture mechanics of materials chapter ten design and failure igure 10.1c) subjects the base of the sign to both bending and torsional loads. Tins chapter synthesizes and applies the concepts developed 111 the previous nine chapters to thedesign of structures subjected to combined loading.hiritilfoai Itipf/A'AviacnluJoiiA10.1COMBINED LOADINGWe have developed s Lecture mechanics of materials chapter ten design and failure eparately the theories for axial members (Section 4.2). for the torsion of circular shafts (Section 5.2). and for symmcưic bending about the : axis (SLecture mechanics of materials chapter ten design and failure
ection 6.2). All these arc linear theories, which means that the superposition principle applies. In many problems a structural member is subject simuM. VtbkMwhaiilcs of Materials: Design and FailureIV I ■*?!CHAPTER TENDESIGN AND FAILURELearning objectives1.Learn the computation of stresses and stra Lecture mechanics of materials chapter ten design and failure at a point.Equations (10 1). (10.2). (10.3a). and (10.3b). listed here for convenience as Table 10 1 summarizes the stress formulas derived in earlier chapters. Equations (10.4a) and (10.4b) extend of the formulas for symmetric bending about the : axis [Equations (10.3a). and (10.3b)] to symmetric Lecture mechanics of materials chapter ten design and failure bending about the r axis as we shall see in Section 10.1.3.Àuạuit 2ŨI2M. VableMechanics of Materials: Design and FailureIVI Wdirection. Recall thai thLecture mechanics of materials chapter ten design and failure
e fust subsciipt ill each stress component is the direction of the outward normal to the surface on which the stress component acts. Thus r}, which acM. VtbkMwhaiilcs of Materials: Design and FailureIV I ■*?!CHAPTER TENDESIGN AND FAILURELearning objectives1.Learn the computation of stresses and stra Lecture mechanics of materials chapter ten design and failure rfaces at points A and c have outward normals in the : dil ection. and hence ra = 0. Thus. is also zero at these points, irrespective of the loading.10.1.1Combined Axial and Torsional LoadingFigure 10.3 show the axial and torsional suesses on stress cubes at points J. B. c. and D due to individual l Lecture mechanics of materials chapter ten design and failure oads. When both axial and torsional loads are present together, we do not simply add the two stress components Rather we superpose or add the two streLecture mechanics of materials chapter ten design and failure
ss states.What do we mean by superposing the stress states? To answer the question, consider two stress components and atpoint c. In axial loading. ợwM. VtbkMwhaiilcs of Materials: Design and FailureIV I ■*?!CHAPTER TENDESIGN AND FAILURELearning objectives1.Learn the computation of stresses and stra Lecture mechanics of materials chapter ten design and failure total state of stress at point c is ợu= ạ^-0 =Lecture mechanics of materials chapter ten design and failure
d associated Mohr circle.hiríCilhsta : liipt'faxvra cialUA*ỉx' <«:f/iNt'M(M2td 111•’iguif 10.4 Stresses in combined axial and torsional loading.Aujuu M. VtbkMwhaiilcs of Materials: Design and FailureIV I ■*?!CHAPTER TENDESIGN AND FAILURELearning objectives1.Learn the computation of stresses and stra Lecture mechanics of materials chapter ten design and failure low cylinder subjected to a load that bends the cylinder about the: axis Points B and D arc on the free surface. Hence the bending shear stress is zero at these points. Points A and c are on the neutral axis, and hence the bending normal stress is zero ar these points. The nonzero sttess components Lecture mechanics of materials chapter ten design and failure can be found from the formulas m Table 10.1. as shown on the stress cubes m Figure 10.5«. If we superpose the stress states for bending ar the four poLecture mechanics of materials chapter ten design and failure
mts shown m Figure 10.5« and the stress stales for the combined axial and torsional loads al the same points shown in figure 10.1. we obtain the SƠCSSM. VtbkMwhaiilcs of Materials: Design and FailureIV I ■*?!CHAPTER TENDESIGN AND FAILURELearning objectives1.Learn the computation of stresses and stra Lecture mechanics of materials chapter ten design and failure 5«. the bending normal stress at point D is compressive, whereas the axial stress in Figure 10.4 is tensile Thus, the resultant normal stress is the difference between the two stress values, as shown in Figure 10.5b. At point B both the bending normal stress and the axial stress are tensile, and thu Lecture mechanics of materials chapter ten design and failure s die resultant normal Stress ơa is the sum of the two stress values. If the axial normal Stress at point D is greater than the bending normal stress,Lecture mechanics of materials chapter ten design and failure
then the total normal stress at point D will be in the dứcction as shown m Figure 10 55. If the bending nonnal stress is greater than the axial sfresM. VtbkMwhaiilcs of Materials: Design and FailureIV I ■*?!CHAPTER TENDESIGN AND FAILURELearning objectives1.Learn the computation of stresses and stra Lecture mechanics of materials chapter ten design and failure in Figure 10.4 is downward. whereas the bending shear sưcss in Figure 10.5« is upward. Thus, the resultant shear stress Eg is the difference between the two stress values, as shown ill Figure 10.55. At point c both the torsional shear stress and the bending shear stress are upward, and thus the res Lecture mechanics of materials chapter ten design and failure ultant shear stress fjj is the sum of the two stress values. If the (sending shear stress at point A is greater than the torsional shear stress, thenLecture mechanics of materials chapter ten design and failure
the total shear stress at point A will be in the direction of positive r„. as shown in Figure 10.55. If the torsional shear stress is greater than theM. VtbkMwhaiilcs of Materials: Design and FailureIV I ■*?!CHAPTER TENDESIGN AND FAILURELearning objectives1.Learn the computation of stresses and stra Lecture mechanics of materials chapter ten design and failure tric Bending about r AxisM. VtbkMwhaiilcs of Materials: Design and FailureIV I ■*?!CHAPTER TENDESIGN AND FAILURELearning objectives1.Learn the computation of stresses and straGọi ngay
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