Lecture mechanics of materials chapter seven deflection of symmetric beams
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Lecture mechanics of materials chapter seven deflection of symmetric beams
M. VabteMechanics of Materials: Deflection of Symmetric Beams71 325CHAPTER SEVENDEFLECTION OF SYMMETRIC BEAMSLearning Objective1.Learn to formulate an Lecture mechanics of materials chapter seven deflection of symmetric beams nd solve the boundary-value problem for the deflection of a beam at any point.Greg Louganis. the American often considered the greatest diver of all time, has won foru Olympic gold medals, one silver medal, and five world championship gold medals. He won both the springboard and platform diving comp Lecture mechanics of materials chapter seven deflection of symmetric beams etitions 111 the 1984 and 19SS Olympic games. In his incredible execution. Louganis and all divers (Figure 7.1a) makes use of the behavior of the diviLecture mechanics of materials chapter seven deflection of symmetric beams
ng board The flexibility of the sprmgboard. for example, depends on Its thill aluminum design, with the roller support adjusted to give just the rightM. VabteMechanics of Materials: Deflection of Symmetric Beams71 325CHAPTER SEVENDEFLECTION OF SYMMETRIC BEAMSLearning Objective1.Learn to formulate an Lecture mechanics of materials chapter seven deflection of symmetric beams ffness in a bridge is obtained by using steel girders with a high area moment of inertias and by adjusting the distance between the supports In each case, to account for the right amount of flexibility or stiffness in beam design, we need to determine the beam deflection, which is the topic of this Lecture mechanics of materials chapter seven deflection of symmetric beams chapterFigure 7.1 Examples of beam (a) flexibility of diving board; and (b) stiffness of Steel girders.We can obtain the deflection of a beam by integLecture mechanics of materials chapter seven deflection of symmetric beams
rating either a second-order or a fourth-order differential equation. The differential equation, together with all the conditions necessary to solve fM. VabteMechanics of Materials: Deflection of Symmetric Beams71 325CHAPTER SEVENDEFLECTION OF SYMMETRIC BEAMSLearning Objective1.Learn to formulate an Lecture mechanics of materials chapter seven deflection of symmetric beams ong the length of the beam7.1 SECOND-ORDER BOUNDARY-VALUE PROBLEMhirícilhoi lỂlịtiVavrưii cnluoỉi' (•.r/iNfc'MtMhdlilChapter 6 considered the symmetric bending of beams. We found that if we can find the deflection in the V direction of one point on the cross section, then we know the deflection of a Lecture mechanics of materials chapter seven deflection of symmetric beams ll points on the cross section. In other words, the deflection at a cross section is independent of the V and : coordinates However, the deflection caLecture mechanics of materials chapter seven deflection of symmetric beams
n be a function of X. as shown 111 Figure 7.2.The deflected curve represented by v(x) is called the elastic cun e.Figure 7.2 Beam deflectionAopMt 2612M. VabteMechanics of Materials: Deflection of Symmetric Beams71 325CHAPTER SEVENDEFLECTION OF SYMMETRIC BEAMSLearning Objective1.Learn to formulate an Lecture mechanics of materials chapter seven deflection of symmetric beams and solution of a boundary-value problem with one second-order differential equation and the associated boundaiy conditions•Example 7.2 demonstrates the formulation and solution of a boundary-value problem with two second-order differential equations, the associated boundary conditions, and the con Lecture mechanics of materials chapter seven deflection of symmetric beams tinuity conditions.•Example 7.3 demonstrates the formulation only of a boundary-value problem with multiple second-order differential equations, the aLecture mechanics of materials chapter seven deflection of symmetric beams
ssociated boundary conditions, and the continuity conditions.•Example 7.4 demonstrates the formulation and solution of a boundary-value problem with vM. VabteMechanics of Materials: Deflection of Symmetric Beams71 325CHAPTER SEVENDEFLECTION OF SYMMETRIC BEAMSLearning Objective1.Learn to formulate an Lecture mechanics of materials chapter seven deflection of symmetric beams intensity of the I = 600 (10*1 nun4. and L = 8 m.as shown in Figure 7.5. Determine. (a) The equation of the elastic curve in terms of £. I, disuibuted load if the maximum deflection is to be limited to 20 mm. Use £ = 200 GPa.Figure 7.5 Beam and loading in Example 7.1.PLAN(a) We can make an imaginar Lecture mechanics of materials chapter seven deflection of symmetric beams y cut at an arbitrary location X and draw the fiee-body diagram Using equilibrium equations, the moment .V. can be written as a function of X. By inteLecture mechanics of materials chapter seven deflection of symmetric beams
grating Equation (7.1) and using the boundary conditions that deflection and slope at X = L are zero, we can find v(x). (b) The maximum deflection forM. VabteMechanics of Materials: Deflection of Symmetric Beams71 325CHAPTER SEVENDEFLECTION OF SYMMETRIC BEAMSLearning Objective1.Learn to formulate an Lecture mechanics of materials chapter seven deflection of symmetric beams w„,iV.SOLUTIONhirícilhxa llipửAMVia train ui VLecture mechanics of materials chapter seven deflection of symmetric beams
in Example 7.1. (a) Imaginary cut on original beam, (b) Statically equivalent diagramM. VabteMechanics of Materials: Deflection of Symmetric Beams71 325CHAPTER SEVENDEFLECTION OF SYMMETRIC BEAMSLearning Objective1.Learn to formulate anM. VabteMechanics of Materials: Deflection of Symmetric Beams71 325CHAPTER SEVENDEFLECTION OF SYMMETRIC BEAMSLearning Objective1.Learn to formulate anGọi ngay
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