Question please help me 1. Derive the governing equation for beam structures (as shown in Fig. 1) by differential formulation and write down the boundary conditions. 2. Following Problem 1, derive the governing equation by variational formulation and determine the natural boundary conditions. 3. Following Problem 1, find an approximate solution for the deflection of the cantilevered beam using Ritz method. 4. As shown in Fig.2, a non-uniform bar is subjected to an axial load of 100 N. Derive the governing equation for axially loaded members and determine the exact solution. W Vmax x - Omax Fig. 1 # Area - 1 cm? Area = (1 +48)2 cm? R-100 N . 100 cm - 80 CM Fig. 2
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Transcribed Image Text: 1. Derive the governing equation for beam structures (as shown in Fig. 1) by differential formulation and write down the boundary conditions. 2. Following Problem 1, derive the governing equation by variational formulation and determine the natural boundary conditions. 3. Following Problem 1, find an approximate solution for the deflection of the cantilevered beam using Ritz method. 4. As shown in Fig.2, a non-uniform bar is subjected to an axial load of 100 N. Derive the governing equation for axially loaded members and determine the exact solution. W Vmax x - Omax Fig. 1 # Area - 1 cm? Area = (1 +48)2 cm? R-100 N . 100 cm - 80 CM Fig. 2
More Transcribed Image Text: 1. Derive the governing equation for beam structures (as shown in Fig. 1) by differential formulation and write down the boundary conditions. 2. Following Problem 1, derive the governing equation by variational formulation and determine the natural boundary conditions. 3. Following Problem 1, find an approximate solution for the deflection of the cantilevered beam using Ritz method. 4. As shown in Fig.2, a non-uniform bar is subjected to an axial load of 100 N. Derive the governing equation for axially loaded members and determine the exact solution. W Vmax x - Omax Fig. 1 # Area - 1 cm? Area = (1 +48)2 cm? R-100 N . 100 cm - 80 CM Fig. 2
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Answer Given Data:uniform dispributed load is omega. Cantilluer beam.Consider tho figure (1) from the guestion.Consider a rection xx at a distana x from the free end as shown in above figure.Find the bending moment at the distance. x.M_(x)=-(omega x)xx(x)/(2)=-(wx^(2))/(2)un'te the bending moment in the term of the differential equation.M_(x)=(EIdel^(2)y)/(dx^(2))=-(omegax^(2))/(2)Integate the equation (1){:[int E(d^(2)y)/(dx^(2))=int(omegax^(2))/(2)dx],[" EI "(dy)/(dx)=-(omegax^(3))/(6)+A]:}Integrate tho equation (2) w.ritin{:[EI int dx=int(-(omegax^(3))/(6)+A)dx],[EI=-(omegax^(4))/(24)+Ax+Delta-" ( ) "]:}Write down tho boundany condition. ... See the full answer