INTRODUCTION In this project, our group decided to choose the chapter multiple integral in mathematics engineering 3 using method in subject Mechanic of Material to solve deformation of statically determinate structure. When the load applied on the beam, it is often helpful to sketch the deflected shape before the slope or displacement at any point on a beam can be determined. This deflection diagram called as an elastic curve. However it is necessary to know how the slope or displacement is restricted at various types of supports. The zero displacement occurs at all pin and roller support. The zero slope and zero displacement occur at all fixed supports and zero displacement occurs at all pin and roller support.
OBJECTIVE This chapter will discuss various methods for determining the deflection and slope at specific points on determinate beam. The methods include the Double Integration method and Macaulay method. Also a graphical technique called the moment area method.
PROBLEM STATEMENT To find deflection and slope at specific points on determinate beam.
Force deflection Shear deflection Bending moment deflection Slope deflection
EXPECTED OUTCOMES Sketch the deflected shape before the slope or displacement at any point on a beam can be determined. We defined the deflection and slope at specific points on determinate beam using double and triple integration. We also defined force deflection, shear deflection, bending moment deflection and slope deflection equation.
CONCLUSION What we found from this study, with their Multiple Integral method we can help to solve in the Mechanic of Materials subject it is Deformation of Statically Determinate Structure. From this method, it helps to facilitate solving this problem to get the desired value ( Shear Deflection Equation, Bending Moment Deflection and Slope Deflection Equation). Engineering Mathematics III proved useful to simplify the scope of engineering.
