The deflection y, in a simple supported beam with a uniform load q and a tensile load T is given by dx2 El 2EI Wher...
2. The governing differential equation that relates the deflection y of a beam to the load w ia where both y and w are are functions of r. In the above equation, E is the modulus of elasticity and I is the moment of inertia of the beam. For the beam and loading shown in the figure, first de m, E = 200 GPa, 1 = 100 × 106 mm4 and uo 100 kN/m and determine the maximum deflection. Note...
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...
Q2. A simply supported beam AB (Figure 2) supports a uniformly distributed load of q = 18kN/m and a concentrated load of P = 23kN at the centre. Consider length of the beam, L = 3m, Young's modulus, E = 200GPa and moment of inertial, I = 30 x 10 mm-. Assume the deflection of the beam can be expressed by elastic curve equations of the form: y(x) = Ax4 + Bx3 + Cx2 + Dx + E. 1) Sketch...
The equation of the elastic curve (deflection) for a simply supported beam under uniform load is given by y= 1.7 * 10^-5 x^2 (160 - x^2 + x^3), in which, x is the distance from the left support of the beam to any point on the beam, and y is the deflection, both in meters. Find the rate of change of the deflection of the elastic curve at x m = 2
can you help me to do BEAM DEFLECTION lab report with data and follow all steps answe all sections below too? Thank you this is beam lab report. data below with formula the formula we need to calculation for section B fill up information for section A calculation percentage error for section C and write discussion and conclusion for section D. Beam Length [in] h=Beam cross section height [in] b=Beam cross section width [in] L =Distance between supports [in] a=Load...
QUESTION 4 (25 marks) A simply supported beam is loaded by an uniform distributed load, wkN/m, over the span of the beam, L, as shown in Figure Q4. (a) Determine the end reactions at point A and B in terms of w and L. (4 marks) (b) At an arbitrary point, x, express the internal mom (c) Show that the deflection curve of the beam under the loading situation is ent, M(x), in x, w, and L. (5 marks) 24EI...
Q5. The cantilever beam, AC, is subjected to the load case shown in Figure 5. For the loading shown, do the following: [10 Marks] a) Calculate the magnitude and direction of the reactions at A b) Using the Macaulay function, determine the displacement in y of the point B of the beam (x 2.4 m from the support at A) [10 Marks] c) Determine the slope at B. [5 Marks] The beam has a Young's modulus of E-200 GPa and...
SOLVE USING MATLAB PLEASE THANKS! The governing differential equation for the deflection of a cantilever beam subjected to a point load at its free end (Fig. 1) is given by: 2 dx2 where E is elastic modulus, Izz is beam moment of inertia, y 1s beam deflection, P is the point load, and x is the distance along the beam measured from the free end. The boundary conditions are the deflection y(L) is zero and the slope (dy/dx) at x-L...
Problem 2 Consider a simply supported symmetric I beam ABCD carrying a uniformly distributed load w and a concentrated load F as shown in Figure 2. Young's modulus of the beam is 200 GPa. F 8 kN 8cm 3cm 3cm 7 m 5 m 3 m 2cm W= 6 kN/m 6cm A D B 2cm 7TITT TITIT Figure 2 1) Replace the support C with the reaction force Rc, and using static equilibrium find the reactions at point A and...
Problem 2 Consider a simply supported symmetric I beam ABCD carrying a uniformly distributed load w and a concentrated load F as shown in Figure 2. Young's modulus of the beam is 200 GPa F- 8 kNN 8cm 3cm 3cm w- 6 kN/m 6cm 2cm Figure 2 1) Replace the support C with the reaction force Rc, and using static equilibrium find the reactions at point A and B in terms of Ro 2) Using the boundary conditions, calculate the...