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Course materials, Books, Computer software, Quiz, Conferences, Journals, Research theses, Jobs, Products, Services etc. Wednesday, February 17th, 116 Deflection of pinjointed planeTruss by Unit Load method
Problem 75 A pinjointed truss is shown in figure 75(a). Determine the vertical displacement of joint E by using unit load method. All the members have crosssectional area of 250 mm2 and same modulus of elasticity 200GPa.
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Figure 75(a) Solution: According to unit load method the deflection of a joint of truss is given by the following formula δ E = (Σ NnL)/AE Here we have to find the member forces two times. First we will calculate member forces "N" due to the real loading and then "n" due to unit virtual load applied at the point of required deflection (in this case joint E).
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Step 1: The member forces "N" due to real load are calculated in Problem SolverNew Example 31 .So, we take those values. A collection of illustrated solved examples for civil engineers. RC Beam CalculatorNew Calculate the strength of reinforced concrete beams Bending Moment calculatorNew
Figure 75(b)
Step 2: Calculation of member forces "n" due to unit virtual load applied at E as shown in figure 75(b). As the unit load is applied at center of the truss, the support reactions at A and C will be 0.5 kN each. Considering the equilibrium of joint D, we get FDE =0 and FDC =0; Similarly the equilibrium conditions at joint F gives; FFE =0 and FFA =0. Consider the equilibrium of joint B along yaxis we get FBE =0. Now consider the equilibrium of joint A. Σ Fy = 0; http://civilengineer.webinfolist.com/str/prob75.htm
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Deflection of Truss by unit load method HorizonNew Online Civil Engineering Journal and Magazine
FAE sin45 + Ay FAF = 0 (i) FAE sin45 + 0.5 0 =0 Therefore, FAE = 0.5/sin45 = 0.707 kN Σ Fx = 0; FAE cos45 + FAB = 0 (ii) Therefore, FAB = FAE cos45 =0.5 kN As the loading is symmetric, the equilibrium of joint C will also yield the forces similar to the member forces at A Therefore, FCE = 0.707 kN, FCB = 0.5 kN All the calculated values are entered in Table 75 Σ NnL =129.9 kN2 m External virtual work = Internal virtual work 1 kN. δE = (Σ NnL)/AE δE = 129.9/[(250x106)(200x106)] vertical deflection at E =0.0026 m = 2.6 mm (Ans) Tweet +51 including You
Table 75 Result of Member Forces Calculations Member N (kN) n (kN) L (m) NnL (kN2 m) AB 22.5 0.5 2 22.5 AF 25 0 2 0 AE 31.82 0.707 2.83 63.67 BC 22.5 0.5 2 22.5 BE 20 0 2 0 CD 0 0 2 0 CE 10.61 0.707 2.83 21.23 DE 15 0 2 0 EF 0 0 2 0
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