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- of A square plate (a x a) is a fixed supported on all four edges and carries a uniform load a (per nit area). The equation for deflection is: V"w=q/D where D is flexural rigidity. Take a h=Ax = Ay =-. Find the deflection at internal nodes. %3D 4Problem 1. Determine the vertical displacement of joint A. Each bar is made of steel and has the cross-sectional area shown. Take E = 29,000 ksi. Use the method of virtual work. A 10 k to 056 2 in² 3 in² 10 ft E 3 in² an@d B os /olee 2 in² 2 in² 3 in² 10 ft Figure 1 Problem 2. Solve Problem 1 using Castigliano's theorem. 6 k D 3 in² 10 ft сQ1 Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial displacement, i.e. EA>>) for the beam shown below. Form member and structure stiffness matrices and compute displacements, reactions and internal forces in the beam under the applied load. Draw the SFD and BMD. Note that there is a hinge at B. Take E = 200 GPa, IAB = 2000 cm4, IBC = ICD= 1000 cm4. A 20 kN OB |1m|1m 6 kN/m 6 m 2 m 10 kN.m
- A tapered bar AB of solid rectangular cross-section with a thickness of 20 mm and length L = 800 mm is supported at the end B and subjected to tensile load P = 25 KN at the free end A. The width of the bar at ends A and B are 50 mm and 75 mm, respectively. Determine the elongation of the bar due to load P. Use E = 200 x 10° Pa. Use integration to solve this problem. В A P < L-Problem 5 Using the conjugate-beam method, determine the displacement at D and the slope at D. Assume A is fixed support, B is a pin, and C is a roller. Take E = 29×10³ ksi, I = 650 in ¹. 12 ft- B -12 ft Ic 12 ft- 24 kUsing Conjugate-Beam Method, determine the displacement at B. 12 m I 80 KN B E = constant = 200 GPa I=600 (106) mm² 12 m 21
- Determine the horizontal displacement of joint D of the truss as shown. Take E = 29(103) ksi. The cross-sectional area of each member is indicated in the figure.The rigid bar BC is supported by the steel rod AC of cross-sectional area 0.27 in2. Find the vertical displacement (in inches and absolute value) of point C caused by the 2448-lb load if x = 9.5 ft and θ = 41.7ᵒ. Use E = 29147 ksi for steel. Note: Round off the final answer to four decimal places.Determine the vertical displacement of joint A. The cross-sectional area of each member is indicated in the figure. Assume the members are pin connected at their end points. E =29 (10)3 ksi. 2 in E 2 in? 2 in? 3 in? 3 in? 4 ft A 3 in? bod 3 in? 4 ft 4 ft 7 k 3k
- Determine the vertical displacement of joint A. The cross-sectional area of each member is indicated in the figure. Assume the members are pin connected at their end points. E =29 (10)3 ksi. 2 in 2 in? 2 in? 3 in 3 in 4 ft B 100 3 in? 3 in 4 ft 4 ft 7k 3kThe cross sectional area of each member of the truss shown in the figure is A = 500 mm^2 and E = 200 Gpa. Use Catigliano's Theorem. Determine the vertical displacement of joint C if a P force is applied to the truss at C If no loads act on the truss, what would be the vertical displacement of joint C if member AB were 8 mm too short.(use data at ¶N/¶P) If P force and fabrication error are both accounted, what would be the vertical displacement of joint CA truss is subjected to loads as shown. Assume AE is constant and use virtual work method for deflection of truss. 4m 120 KN B A TINT 3m EA = constant E = 200 G Pa 2 A = 1,500 mm Find the vertical deflection at B in mm