Problem 2 (30 points): The formula for the deflection of the beam shown is: y(x) = Wo (-x5 + 5Lx*- 10L²X3 + 10L3x2) 120LEI Wo = 15 x 107 N L = 2m Omax %3D %3D т N E = 7 x 1011. m2 1 = 6 x 10-4m %3D %3D Use the Newton-Raphson Method to determine the x location along the beam where the deflection is y(x) = 0.14 m. Use a starting guess of xo = 1.2 m. Be sure to show your calculation for the derivative of the function and your calculations you use to fill out the table. You only need to perform two iterations of the method, which means you should fill out the table below. Notice that y is defined as positive in the downward direction, which means that both the function and the target deflection are positive values in the coordinate system. y(xn) y'(xn) Хn+1 Step Xn 2

Problem 2 (30 points): The formula for the deflection of the beam shown is: y(x) = Wo (-x5 + 5Lx*- 10L²X3 + 10L3x2) 120LEI Wo = 15 x 107 N L = 2m Omax %3D %3D т N E = 7 x 1011. m2 1 = 6 x 10-4m %3D %3D Use the Newton-Raphson Method to determine the x location along the beam where the deflection is y(x) = 0.14 m. Use a starting guess of xo = 1.2 m. Be sure to show your calculation for the derivative of the function and your calculations you use to fill out the table. You only need to perform two iterations of the method, which means you should fill out the table below. Notice that y is defined as positive in the downward direction, which means that both the function and the target deflection are positive values in the coordinate system. y(xn) y'(xn) Хn+1 Step Xn 2

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

For the given 2D element shown in the diagram with positions A = 5 m and B = 5 m, answer the following: a) X (0,B) 1 2 (0,0) 3 (A,B) DIAGRAM NOT TO SCALE Write the expression of basis function associated with point 1, in terms of x and y Submit part Unanswered b) The displacement of node 3 is 0.3 m in the x direction, and 0 in the y. All other node displacements are zero. What is the normal strain component across the element? Submit part Unanswered
Mechanics of deformable bodies: shear and moment diagram in beams. From the given figures below, draw the shear and moment diagram of the beam. Its either using the shear and moment diagram or area method. Please show the solving solution also.
Question 3 A simply supported beam with the boundary conditions as shown. An applied load, F is acted at the center of the beam and causes a deflection, y in meter. Using the value from the Table to plot a graph and using the moment of area and cantilever beam theory to determine the value of Young's Modulus, E of the beam in N/m². The following data are obtained in a simple experiment: F(N) y(m) 0 0 2.45 0.00043 Given that the moment of area, I=4.572x 10-10m4 The length of the beam, L = 0.25m FL3 According to the cantilever beam theory: y = - 48EI 14.71 4.9 7.36 9.81 12.26 0.00087 0.00131 0.00175 0.00218 0.00262 F L/2 40 Points I www
A A squere plate is boended by the liner x = ±2, y= ± 2. The boundlary femperatures %3D are on the hine y=2, T=-8o on the line x-12,T=-40Y on the line y=-2, T= 240 + 8ox for -25x Ko 7 = 240 - 8o x tor o
Assign the values of shear force and bending moment to the image bar as a function of the x coordinate. q=20kN/m F=14kN M=12kNm L1=1.2m L2=1.4m L3=1.3m L4=1.5m Minimum value of shear force: Qmin = Maximum value of shear force: Qmax= Use units (kN,m), Do not round the invoices in the intermediate stages, but only the final answer!
Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a=4.0 ft, b-9.0 ft. c=4.0 ft, d=3.0ft, w=8 kips/ft and P = 66 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. B B ÎÎÎÎÎÎ Answers: Ay=i b d For this loading, calculate the reaction forces Ay and Ey acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) W C b C C D E kips, Ey = i E X Ey kips.
Q1 The stiffness matrix for a Timoshenko beam-column element in its local coordinate system (where x is along the beam length) is: L²A L²A ī(1+$) -7 (1+ 4) 12 6L -12 6L E I 6L L²(4 + ¤) -6L L(2 – 4) [K'] = L²A (1 + 4) L³ (1 + Ø) L²A (1+ ø) I -12 -6L 12 -6L 6L L²(2 – $) -6L L2(4+ ¢)] 12EI GAŞL? a) Derive the transformation matrix [T] for this element, such that the stiffness matrix of the element can be transformed to the global coordinate system using the following relation: [K«] = [T<]*[K¢°][Te]
Points for stress vs strain (in image) Assume the compressive concrete strength (f’c) is 3,000 lb/in2 (psi)Calculate a cubic function (3rd order polynomial – Ax3+Bx2+Cx+Constant)Use this function to create a function that describes the slope of the cubic function (the derivative of thecubic function). This new function allows you to calculate the tangent to any point along the curve. Thetangent is the modulus of elasticity (E). The concrete code provides a formula to calculate E for concrete. That formula is:E = 57,000√??′, where f’c is in units of psi, and E is in units of psi.Use the derivative function you calculated to locate the point on the curve where the slope of the curvematches E using the concrete code formula. Express that stress point on the curve as a percentage ofthe compressive strength of the concrete. Now, calculate the secant modulus for the test case using 1,500 psi (50% f’c) as the arbitrary point onthe curve.Assume fracture occurs at the last point…
Solve; y" +4y' + 3y = 0 y(0) = 3 & y'(0) = 1 %3D
solve, show all steps and fbd. do not provide copied answer or I will report Do problem 12 -22 using double integration. Also find how much additional deflection is added (to the max) if we account for the beam self-weight. Find this additional deflection using the table in appendix C. mechanics of materials chapter 12 (integration of moment)= theta, and integration of theta = v
Q: Figure 2 shows a typical mast from a modern racing yacht. It is built in the form of a thin-walled tube (hallow cylinder). To win long-haul ocean races, these yachts need to have every advantage that high-performance materials can give, in terms of maximum stiffness (must not easily deflect), plus minimum weight as possible. The following are the equations to use: 1(F13 8 == 8 EI and I = ar³t, A = 2art assume l and cross section are fixed but thickness t is free to change. • Drive the performance index for this problem • Use table 1 to select top three materials with the best performance index. Figure 2 Table. 1 Data for Tube of Given Stiffness p (Mg.m 3) 2.0 Material E (GPa) GFRP 12 Steel 7.8 200 Wood 0.6 12 Aluminum alloy Titanium alloy 2.7 69 4.5 120
Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a=3.5 ft, b=9.0 ft, c=4.0 ft, d=3.5 ft, w = 5.5 kips/ft and P = 45 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. For this loading, calculate the reaction forces Ay and Ey acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) Ay =___________ kips, Ey = __________ kips. Determine the shear force acting at each of the following locations:(a) x = 0+ ft (i.e., just to the right of support A)(b) x = 3.5 ft(c) x = 12.5 ft(d) x = 16.5– ft (i.e., just to the left of D)(e) x = 16.5+ ft (i.e., just to the right of D)(f) x = 20.0– ft (i.e., just to the left of support E) Answer: a to f ) V = ________ kips Use the graphical…