Q-2 Use the method of superposition to determine the deflection at the free end of the cantilever beam shown when w = 7.5 kN/m, L = 3 m, I = 180e6 mm² and E = 200 GPa.. Bonus: Validate your results using singularity functions 3 w N/m 3wL2 N-m w N/m Lm 2 Lm
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- Assume portion ABC of the rod is made of steel (E4e= 200 GPa , v=0.3) and portion CD is made of aluminum (E,lumi = 70 GPa , v=0.25). A 1.75 m Area = 800 mm² 120 kN B 1.25 m C Area = 500 mm² 1.5 m 80 kN D 60 kN The deflection of point C is_ The resulting change in diameter of portion AB of the bar is_For the beam shown, use only singularity functions. V₁ = 45 lbf/in and V/₂ = 5 in. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 0 1400 lbf Hinge JA B₁ C R₂ R₁ 4 in 4 in 2 in V1 V2 D R₂ + What is the value of the peak moment between points Cand D? The peak moment between points C and Dis Ibf.in.For the vertical rod as shown, find the deflection at A and the stress distribution. Use E-100 MPa and weight per unit volume equal to 0.06 N/cm3. (Hint: Introduce weight contribution to the nodal loads and solve using two elements and four elements.) Comment on the stress distribution. a) Use 2 & 4 elements with linear shape functions. b) Use 2 elements with quadratic shape functions. 1.6m C A -Area - 2500 cm² 8 Area - 1500 cm²
- A beam of uniform rectangular section 200 mm wide and 300 mm deep is simply supported at its ends. It carries a uniformly distributed load of 9 KN/m run over the entire span of 5 m. if the value of E for the beam material is 1 X 104 N/mm2 , find the slope at the supports and maximum deflection. Give me complete solution based on the given above. Again I need to ask the same question since you gave me a wrong answer before.2. L=3m 16mm dia. E=200GPA W 5 m 5 m I=10x106 mm When the deflection of the rod is 1mm, compute the force P of the rod.The beam ABC made of steel is receiving a point load P at the right end C. Please solve two problems from d to e. (a) Find the reaction from the supports A and B.(b) Use the double integration method to express the deflection y for the beam AB part as an equation for x (including E, I, P, a, L).(c) And use the following values to express the maximum value ymax of the deflection at the beam AB as mm. (Figure: I=300x106 mm4, E=200 GPa, P=200 kN, L=4.5 m, a=1.2 m)(d) Using the singularity function method, express the deflection y for the entire beam ABC as the equation for x (including E, I, P, a, L).(e) And use the following values to represent the deflection value yC at the right end part C as mm. (I=300x106 mm4, E=200 GPa, P=200 kN, L=4.5 m, a=1.2 m)
- For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the slope at A, (c) the slope at B, and (d) the deflection at midspan. Assume that El is constant for the beam. Let Mo = 50KN-m, L= 4.5 m, E= 180 GPa, and I = 115x 106 mm4. Mo B Answer: (b) 0A = i rad (c) Og = i rad (d) vmid = i mmThe part shown is formed from a 1/8 - in diameter steel wire, with R = 2.5 in and l = 2 in. A force is applied withP = 1 lbf. Use Castigliano's method to estimate the horizontal deflection at point A. Justify any components ofstrain energy that you choose to neglect.Q 4: Using Castigliano's method for Determining the vertical deflection at A for the lamp post loaded as shown in Fig. (4). Take EI=constant. Figure (4) L
- Q2 Find the deflection at the tip of the cantilever shown in figure below. Use EI=20MNm². 1m 30kN/m 10kN 1m 25kNQ2: A simply supported beam as shown below. Determine the deflection at C and D. Take E = 210 GN/m? and I = 16 x10% mm*. 120 kN 80 kN -0.6 m- 1.4 m C 3 m3. Determine the displacement and slope (i.e. 0) at the load point for the stepped beam shown in the following figure. Also determine the reaction forces and moments. Each element has E = 200 GPa. The area moment of inertia are given as I₁ = 1.25 × 105 mm4, and 2 = 4 x 104 mm. Clearly show the elemental stiffness matrices (k) for each element, assembly of k matrices to get global stiffness matrix (K) and application of boundary conditions. Then solve the reduced K matrix to get displacements and reactions 3000 N 150 mm 75 mm 125 mm