14.12 The cantilevered beam shown in the accompanying figure is used to support a load acting on a balcony. The deflection of the centerline of the beam is given by the following equation: -wx? y = -(x²-4Lx+6L) 24 EI where y = deflection at a given x location (m) w = distributed load (N/m) (m) E = modulus of elasticity (N/m²) I = second moment of area (m*) X = distance from the support as shown (x) L = length of the beam (m) ELA maldor Problem 14.12 Using Excel, plot the deflection of a beam whose length is 5 m with the modulus of elasticity of E =200 GPa and I=99.1×106 mm4. The beam is designed to carry a load of 10,000 N/m. What is the maximum deflection of the beam? r sis-

14.12 The cantilevered beam shown in the accompanying figure is used to support a load acting on a balcony. The deflection of the centerline of the beam is given by the following equation: -wx? y = -(x²-4Lx+6L) 24 EI where y = deflection at a given x location (m) w = distributed load (N/m) (m) E = modulus of elasticity (N/m²) I = second moment of area (m*) X = distance from the support as shown (x) L = length of the beam (m) ELA maldor Problem 14.12 Using Excel, plot the deflection of a beam whose length is 5 m with the modulus of elasticity of E =200 GPa and I=99.1×106 mm4. The beam is designed to carry a load of 10,000 N/m. What is the maximum deflection of the beam? r sis-

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter9: Deflections Of Beams

Section: Chapter Questions

Problem 9.2.5P: The deflection curve for a cantilever beam AB (sec figure) is given by...

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Derive the equation for the elastic curve for the depicted beam by first finding M(x) and (x). In addition, find the expressions for the maximum slope and maximum deflection of the beam. This is a symbolic answer and you may take EI to be constant. noc Mo M(x) 0(x) = v(x) = Omax Umax = || = ←X-> L cc is BY NO SA 2022 Cathy Zupke
Q1. A cantilever beam is carrying a UVL of 20000N starting at the free end and extends to 100000N to fixed end over a span of 5000mm. The beam also carries 2-point loads of 1000N and 5000N acting on free end and 2m from free end respectively. The material has the modulus of elasticity of 2.05x10^5 N/mm2. Calculate the deflection for the beam considering an addition UDL of 7kN/m for a span of 2 m starting from fixed support. This beam is made up of a unique shape with a block of 200mm x 250mm which had a top chopped off from top with a radius of 10cm.
For the beam and loading shown, use discontinuity functions to compute (a) the slope of the beam at B and (b) the deflection of the beam at C. Assume a constant value of El = 40 x 10^6 Ib-ft^2 for the beam; wo= 6200 Ib/ft, LAB = 3.0 ft, LBC = 6 ft, LCD = 3 ft.
Problem 2 (30 points): The formula for the deflection of the beam shown is: Wo y(x) = (-x5 + 5Lx-10L?x3 + 10L³x²) 120LEI Wo 15 x 107 N L = 2m %3D max m E = 7 × 1011 N m2 I = 6 x 10-4m 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 %3D 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) Xn+1 Step Xn 2.
Calculate the beam deflection at point C. E = 206.8 GPa, I„ = 1.873 x 10-6 mª. Use either the double integration method or the moment area method. Show your work. 200 N 500 N 50.8 mm -------z 76.2 mm A 1 m 1 m 2 m
A cantilever beam with the fixed support on the left is under the loadings below, w = 6n Note: wn. E (Young's modulus), I (moment of inertia) are constant. Click here to see all formulas Part A- Determine the slope of the beam at x = Woa a is , assuming 4. EI w = 6wo. %3D -0.826 O -1.24 -3.30 O - 2.58 O -2.06
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