PowerPoint PresentationHomework #6Slide 3Slide 4Slide 5Slide 6Relations Between w, V, and MShear ForcesBending MomentsME221 Lecture 15 1ME 221 StaticsLecture #15aSections 7.3 - 7.4ME221 Lecture 15 2Homework #6•Chapter 7 problems:–6, 19 & 26•Chapter 6 problems–3 & 6–Due Monday, June 28•MatLab Group Problems–7.19, 7.26 & 6.15 –Due Monday, June 28ME221 Lecture 15 3Last Lecture:Internal Forces in Structures•Reviewed internal/external forces•Found internal forces•Started shear & moment diagramsME221 Lecture 15 4Generate a shear / bending diagram as follows: 2. Take a section on each side of an applied force or moment and inside a distributed load (take a new section whenever there is a change in the load or shape of the beam)- draw a FBD and sum forces / moments3. Repeat 2 along the length of the beam1. Find reaction forcesw(x) distributed loadV(x) shear forceM(x) momentShear and Moment Diagrams using Sectioning MethodME221 Lecture 15 5VMVMSign Convention Positive Shear and Positive MomentME221 Lecture 15 6Positive ShearMMPositive MomentEffect of External ForcesME221 Lecture 15 7Relations Between w, V, and MIn balancing forces, we can come up with differential equations relating w, V, and M. These are as follows: ,dM x dV xV x w xdx dx This means you can integrate the shear diagram to obtain the moment diagram.dxM+dMMVV+dVw(x) 0)()(0 dxxwdVVVF0)(0 dMMVdxMM Thus,ME221 Lecture 15 8Shear Forces•Area under load curvexduuwxV0)()(ME221 Lecture 15 9Bending Moments•Area under shear force
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