2. The defl ection a uniform beam with flexual rigidity EI and applied. be load f (x) = cos (x) satisfies the equation 2 y(0) =v'(0) = 0 11' (2)イ(2) =0 Ely(4) (x) = f (x) (a) Evaluate the de...
need help for this question in full answer 2. The deflection along a uniform beam with fexual Yigidity BI- and applied load f (x) = cos (-) satisfies the equation (a) Evaluate the deflection y (x). Hint: /cos(az)dz-asin (as)+C, /sin(as)dz=-a cos(az) +C (b) Find the influence function (Green's function) G (z,f), where 0 < ξ < 2, for this problem. Hint: Since 0 < ξ < 2, H(0-E)=0, H(2-E)=1. (c) Hence write the deflection of this beam as a definite...
2. A beam with a uniform flexural rigidity, EI, is loaded by a triangular distributed load, Pz(x), as shown below: a) Find the deflection w(x) (10pts) b) Sketch the shear force V(x) and the beading moment M(x) along the length of the beam, labeling all significant points. (5pts) c) Calculate the maximum bending stress, Omax, and indicate where it occurs. (5pts) z, W Cross Section - 1/3 — * - 2/3 —
Mohammed Abdurahman Active Now The defection slong s uniform beam with fecual rigdity B-andapplied lond f(x)ossatisfis the equation (a) Evaluate the deflection y (a). (b) Find the influence function (Green's function) G(z,0, where 0 < ξ < 2 for this problem. Hint: Since 0 < ξ < 2, H(0-E)=0, H(2-E)-1. (e) Henoe write the deflection of this beam as a definite integral. Do not attempt tp evaluate the integral. ((7+2+2)+(6+6+2)-25 marks) Repl Crop Share Scroll Draw capture Mohammed Abdurahman Active...
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0 4. (a Let (sin( x cos( ) dr...
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) - (sin t, cos t, sin 2t), 0 s t s 27. (Hint: Observe that C lies on the surface z - 2xy.) F dr- 6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) -...
Case 1: Uniform beam under distributed load.In the shown Figure, a uniform beam subject to a linearly increasing distributed load. The deflection \(y(\mathrm{~m})\) can be expressed by \(y=\frac{w_{o}}{120 E I L}\left(-x^{5}+2 L^{2} x^{3}-L^{4} x\right)\)Where \(E\) is the modulus of elasticity and \(I\) is the moment of inertia \(\left(\mathrm{m}^{4}\right), L\) length of beam.Use the following parameters \(L=600 \mathrm{~cm}\), \(E=50,000 \mathrm{kN} / \mathrm{cm}^{2}, I=30.000 \mathrm{~cm}^{4}, w_{\mathrm{o}}=2.5\)\(\mathrm{kN} / \mathrm{cm}\), to find the requirements1) Develop MATLAB code to determine the point of maximum deflection...
Show that the function y = cos (ln(x)] satisfies the differential equation 22 day dy +2 dx +y = 0. dc2
n=9 The equation for the deflection along a particular uniform beam under a given load is given by da y cos(x) H(x – 2n7) = with 0 < x < 4nt dr4 y'" (0) = 0, y" (0) = 0, y (4n7) = 0, y(4nn) = 0 dy 1. Integrate once and write down your expression for and then apply the boundary d.p3 condition y" (0) = 0. Write down your value for the integration constant. day 2. Integrate again...
The deflection along a discontinuous cantilever beam of length 4 units is governed y (0)-y' (0) 0 d2y dx2J 4) (4) (a) Show that 1+2H (-2)2) if o < <4 (b) Ealute dr dl e) Evaluate the deflection y(r). the deflection y (r Hint: If F (x) is an antiderivative of f (x) then f (x) H (r-a) dr = F (x)-F (a)] H (z-a) + C. The deflection along a discontinuous cantilever beam of length 4 units is governed...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...