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EG-225: Structural Mechanics II-b CONTINUOUS ASSESSMENT Semester II 1 MatLab code for a two-dimensional truss bridge. For the two-dimensional...

Matlab code for a 2-D Truss.
EG-225: Structural Mechanics II-b CONTINUOUS ASSESSMENT Semester II 1 MatLab code for a two-dimensional truss bridge. For the two-dimensional pin-jointed truss bridge shown in Figure 1 , the Young’s modulus is E = 200GPa and the cross sectional area is A = 1500mm 2 for all truss members. The truss structure is subjected to a varying load F acting downwards in the nodes 6 , 7 , 8 as depicted in Figure 1 . Create a MatLab computer program to: X Y F(kN) F(kN) F(kN) 1 2 3 4 5 6 8 7 5m 5m 5m 5m 5m Figure 1: Truss bridge model 1. (i) Compute the global displacements at all nodes, the reactions at the supports and the axial forces in every truss member for F =20 kN. The results should be displayed in a format similar to the format displayed in Figure 2 . In addition, draw the undeformed shape (in blue) and the deformed shape (in red) of the bridge in the same graph – see Figure 3 . (ii) Draw a cartesian diagram where the vertical displacement at node 7 (i.e. at midspan) is plotted for a varying load F [0 , 200]kN (see Figure 4 ). You must use 10 incremental loading steps in order to plot the curve. Demonstrate that the graph obtained is a straight line and therefore the principle of superposition holds. (iii) Investigate the effect of reducing the cross sectional area of the truss member joining the nodes 4 and 6 and the truss member joining the nodes 4 and 8. You must draw a new cartesian diagram as the one shown in ( Figure 4 ) and compare its slope with the slope of the diagram obtained in (ii). (iv) Investigate the effect of adding two new truss members into the original truss structure as shown in Figure 5 . You must draw again a cartesian diagram as the one shown in Figure 4 and compare its slope with the slope of the diagrams obtained in (ii) and (iii). 1
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(v) Compare some of the results previously obtained by making use of your Mat- Lab computer program with any available structural analysis computational software (i.e. RuckZuck ). Hint : The most complicated part of your stiffness method computer program should be the assembly of the Global Stiffness Matrix (GSM). A hint to carry out this task by using the appropriate global stiffness submatrices K a ij is given below in algorithmic language, %Degrees of freedom per node ndgof=2; %Element connectivity for element iel %node i=first node of element iel %node j=second node of element iel node1=connectivity(iel,1); node2=connectivity(iel,2); %Assembly of submatrix K a ii fr element iel GSM(ndgof*(node1-1)+1:ndgof*(node1-1)+ndgof,ndgof*(node1-1)+1:ndgof*(node1-1)+ndgof)=. .. GSM(ndgof*(node1-1)+1:ndgof*(node1-1)+ndgof,ndgof*(node1-1)+1:ndgof*(node1-1)+ndgof)+. .. lsm(1:ndgof,1:ndgof); Hint : Spend some time thinking in advance how you think the flowchart of the program should look like before you actually start implementing and debugging computer code lines. plane truss Load increment no.= 1 Node OX-coordinates OY-coordinate U-displacement V-displacement Theta-rotation 1 0.0000E+000 0.0000E+000 0.0000E+000 0.0000E+000 2 4.0000E+003 0.0000E+000 0.0000E+000 0.0000E+000 3 0.0000E+000 4.0000E+003 0.0000E+000 0.0000E+000 4 4.0025E+003 4.0000E+003 2.5076E+000 0.0000E+000 Element [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] 1 0.0000E+000 0.0000E+000 0.0000E+000 0.0000E+000 0.0000E+000 0.0000E+000 2 6.2689E+001 0.0000E+000 0.0000E+000 6.2689E+001 0.0000E+000 0.0000E+000 3 0.0000E+000 0.0000E+000 0.0000E+000 0.0000E+000 0.0000E+000 0.0000E+000 4 3.1344E+001 0.0000E+000 0.0000E+000 3.1344E+001 0.0000E+000 0.0000E+000 Node DGOF Reaction 1 1 -2.2164E+001 1 2 -2.2164E+001 2 1 0.0000E+000 2 2 0.0000E+000 3 1 -6.2689E+001 4 2 2.2164E+001 Figure 2: 2D Frame results representative output file. 2
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