Concept explainers
A cylindrical beam carries a compression load
where
Want to see the full answer?
Check out a sample textbook solutionChapter 16 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- The cross section of a bimetallic strip is shown in the figure. Assuming that the moduli of elasticity for metals A and B are EA=168 GPa and EB= 90 GPa, respectively, determine the smaller of the two section moduli for the beam. (Recall that section modulus is equal to bending moment divided by maximum bending stress.) In which material does the maximum stress occur?arrow_forwardMA MB= Mc= MD= Required information For the beam shown, find the reactions at the supports and plot the shear-force and bending-moment diagrams. V=50 lbf/in and V2 = 7 in. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Hinge = 1400 lbf/ A BI AC R₂ R₁ 4 in 4 in 2 in V1 Determine the values of the moments at points A, B, C, and D. lbf.in lbf.in lbf.in Ibf.in V2 D R₂arrow_forwardConsider the beam in the picture below: 7kN/m 5kN/m P N/m Section 1 Section 2 Section 3 - L/3 L/3 L/3 %3D Take P = the last four digits of your student number in N/m. If P<250 N/m then take P = 30OON/m instead. Take L = the third digit of your student number, reading left to reight. If this value is zero then take L = 2 Assume: The reaction at the Pin = V pin 47000L+9PL )N 54 The reaction at the Roller = Vroller = 61000L+9PL 54 and that both reactions act vertically upwards. a) Find an expression for the internal moment for Section 1. Show all working and any relevant free body diagrams. b) What is the maximum magnitude of the internal moment for Section 1? Mark sure you prove that the value you calculate is the maximum. c) Find an expression for the internal moment for Section 2. Show all working and any relevant free body diagrams. d) What is the maximum magnitude of the internal moment for Section 2? Mark sure you prove that the value you calculate is the maximum. e) Find an…arrow_forward
- Consider the following values in the given beam above: L1=6m L2 = 2 m L3 = 4 m L4=3m L5=2 m L6=1m W1 = 90 kN/m W2 = 30 kN/m P = 50 kN M = 60 kN-m Point E is an internal hinge W1 B L2 L3 2 m E W2 L5 L6 Harrow_forwardFor 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.arrow_forwardA uniform beam is simply supported at both ends x = 0 and x = L. Find the shape of the center line of the beam, given the weight per unit Length is w. v(x) = [xª – 4 Lx3 + 6L?x²] 24 EI a. y(x) = [x4 – 2Lx3 + L?x²] 24 EI b. 2AEX1- 2Lx3 + L³x] 24 EI C. v(x) = v(x) = [2x4 -5 Lx3 + 3L?x²] 24 EI d. y(x) = [2x4 - 3L³x3 +3L²x²] е. 24 EIarrow_forward
- 1. A simply supported beam with length of 5 Meters is loaded with a counterclockwise couple of 5 KN.M at I Meter from the left support and a point load of 5 KN at 3 Meters from the left support. The beam is an I-Section with the following dimensions: bf = 250 MM tf = 16 MM tw = 10MM d = 350 MM Determine the MaxiMUM tensile and compressive bending stress developed in the beam. 2. A simply supported beam with a length of 4M is loaded with a uniform distributed load (w). The beam has a rectangular hollow section with the following dimensions: Outer Base = 150 MM Outer Depth = 200 MM Inner Base = 100 MM Inner Depth = 150 mm Determine the maximum uniformly distributed load which can be applied over the entire length of the beam if the bending stress is limited to 8 Mpa.arrow_forwardA uniform beam is fixed at end x=0 and simply supported at x = L. Find the shape of the center line of the beam, given the weight per unit Length is w. a. b. C. e. O y(x) = d. y(x) = a y(x) = y(x) = y(x) = W 24 El -[x4 - 4Lx³ +6L²x²] =[x4-2Lx³ + L²x²] -[x4-2Lx³ + L³x] -[2x4-5Lx³+3L²x²] [2x4-3L³x³ +3L²x²] W 24 El W 24 El W 24 El - W 24 EIarrow_forwardThe beam AB, shown in Figure 1a, with length L = 4.5 m is subjected to a uniform distributed load w = 13 kN/m and a concentrated moment M = 18 kN.m applied at point B. The beam has a rectangular cross-section with height h = 183 mm, width b = 98 mm, and constant thickness t = 12.5 mm as shown in Figure 1b. Take E = 200 GPa. 1.1. Determine the moment of inertia of the cross section. 1.2. Determine the slope at point Barrow_forward
- The shape of the beam made of U profile ensures safe loading. Find the length c of the overhangs so that it can move. Of the material Safety stress (ç) emn = 50 N / mm2 for tension and compression conditions, (ob) emn = 80 N / mm2. Support spacing of the beam L = 6 m, cross section its dimensions are a = %D 210 mm, b = 150 mm and wall thickness t = 40 mm. The loading condition is P = 30 kN and qo = 40 kN / m. P B (Kesit)arrow_forwardDetermine the maximum compressive bending stress (o max.comp.x=2.8) for the beam section at distance 2.8 m from A, for the beam loaded in Figure 5.1la1(b), in N/mm2. The cross section of the beam is shown in Figure 5.1a1(a). Given D = 120 mm, t = 15 mm, location of centroid of the cross section = 62.1 mm from x-axis, second moment of area with respect to its centroidal x-axis (Iy) = 7.08 x 106 mm“, a = 0.9 m, b = 0.9 m, and P1 = 20 kN. (Note: Use negative sign "-" to denote compressive stresses) t; D Figure 5.1a1(a) P, kN A В D a m b m 3 m Figure 5.1a1(b)arrow_forwardThe figure below shows the cross-section of an axisymmetric composite beam that comprises steel (Young's modulus 270 GPa) and aluminum (Young's modulus 90 GPa) sections that are bonded together. The steel section is of wall thickness 15 mm and the aluminum section is of wall thickness 10mm. The steel section comprises 4 axisymmetric holes of 5 mm diameter as shown. Given that the beam is bent by a couple moment of 1200 Nm, determine the maximum stress in steel and aluminum. 4 holes of diameter 5 mm. 12 mm steel aluminumarrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning