Determine the beam cross-sectional areas that result in the minimum weight for the truss we studied in Sec. 12.2 (Fig. 12.4). The critical buckling and maximum tensile strengths of compression and tension members are 10 and 20 ksi, respectively. The truss is to be constructed of steel (density
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Chapter 16 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- 17. Problem 8: The cross-sectional area of each member of the truss is 1200 mm^2. Calculate the stress in member DF in MPa. Indicate if tensile or compressive stress. 6 m 4 m 4 m 3 m E 3m 100 kN 200 kN Your answer 18. In Problem 8, calculate the stress in member EF in MPa. Indicate if tensile or compressive stress. Your answerarrow_forwardA 10-element, 6-node planar truss is shown below. Let A = 0.02 m? and E = 200 GPa for all elements. Note the spring with spring constant k, at node 6. In this quiz, you will essentially duplicate the truss-analysis steps that we have discussed in class during this past week. Note: L=3 m, A=0.02 m², E=200 GPa 150 kN 2 3 3 10 250 5 ks = 600 × 106 N/m kN Your task list is as follows: 1. Draw a neat figure, and show all the nodal primary and secondary variables (i.e., the U's and the F's at each node). 2. Derive the finite element matrix equations for this problem in the form: [K]{U} = {F} where K = B"DB. 3. Apply the boundary conditions, and solve for (i) the unknown nodal displacements, (ii) the un- known reaction force components at each of the supports., and (iii) the unknown forces in each of the elements (i.e., bars).arrow_forwardWrite legibly, provide step by step manual solution, and diagram for below given problem. An iron rod 6m long and 1.6mm2 in cross section stretches 1.2mm when a mass of 315kg is hang on it. Compute the modulus of elasticity of the iron. (Ans. E = 9656.72 Gpa)arrow_forward
- A semi-elliptical spring 800mm long has eight leaves, two of which are full length. Theleaves are 8mm thick and 60mm wide each. It is desired to replace this spring by a helicalcoil spring of 100mm mean diameter and of such nature that for any load it will have thesame induced stress and same deflection as the leaf spring. What should be the diameter ofthe wire?arrow_forwardSolve following the problems below and show your complete, systematic and neat solution. Upload your solution with one PDF file. 1. For the beam shown, a. determine the maximum flexural stresses in compression ant tension. b. determine the flexural stress of the fiber located at 3m from the left support and 50 mm above the bottom 18 kN/m 300 mm 6 kN/m 20 mm 27 kNm 22 2m 2m 3 m +m 15 mm - - 50 mm 360 mm 20 mmarrow_forwardCompute for the force in each member of the truss shown in FIGURE 1 if the members are made of structural steel with a Modulus of Elasticity of 200 GPa and a Coefficient of Thermal Expansion of 12x10^-6. Indicate in your solutions if the force is in tension or in compression.arrow_forward
- A closely coiled helical spring of mean diameter 140 mm is made up of 12 mm diameter steel wire. Calculate the direct axial load, the spring can carry if the maximum stress is not to exceed 100 MPa.arrow_forwardA load is applied to a rigid bar that is symmetrically supported by three steel rods, as shown. The cross-sectional area of each of the rods is 1.2 in2. Calculate the maximum load P that may be applied (a) using an elastic approach with an allowable stress of 22,000 psi and (b) using an ultimate strength approach (inelastic) with a factor of safety of 1.85. Assume a ductile material with a yield stress of 36,000 psi.arrow_forward1. Construct a critical end-load intensity against slenderness ratio graph for a range of pinned columns made from a material having a Young's Modulus of 200 GPa and a yield stress of Use slenderness ratios from 0 to 300. 30ОMPа.arrow_forward
- Eremple 16.1. A solid round bar 60 mm in diameter and 2.5 m long is used as a strut. One of the strut is fixed, while its other end is hinged. Find the safe compressive load for this strut, Euler's formula. Assume E = 200 GN/m? and factor of safety 3. %3Darrow_forwardThe following figure shows the critical position of a crane that supports 2.5 Tons of load by means of a chain. You are delegated the responsibility of building a crane with similar geometric characteristics and load capacity. The diagram of free body of the crane arm can be redrawn as follows. (check the attached image "fbd") Assuming that the crane arm will be made of steel with yield stress sigmaY =220 MPa and that you must consider a safety factor of F.S.=1.5, propose a profile from the following catalog for the manufacture of the crane arm. Ignore the effects of shear forces on this element. On the other hand, it is very important that you consider the effects of axial loads. Commercial profiles for arm construction. (Check image "profiles")arrow_forwardProblem 7.34 Consider the two-member frame shown in (Figure 1) Suppose that w = 2.6 kN/m, w = 1.9 kN/m Follow the sign convention. Figure -1.5m -1.5m 15m 1.5m 1 of 1 Part A Determine the normal force at point E. Express your answer to three significant figures and include the appropriate units. NE- Value Submit Previous Answers Request Answer Incorrect; Try Again; 4 attempts remaining Part B Determine the shear force at point E Express your answer to three significant figures and include the appropriate units. VE = Part C HA Value Mg Value Submit Units Heavest Answ Determine the magnitude of the moment at point E. Express your answer to three significant figures and include the appropriate units. < Return to Assignment Units Pearson ? Units Provide Feedback 16 O ? 6 of 6 Revisearrow_forward
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