6.9 What would be the effect on the end deflection for question 6.7, if the built-in end A were replaced by a simple support at the same position and point B becomes a full simple support position (i.e. the force at B is no longer 10 kN). What general observation can you make about the effect of built-in constraints on the stiffness of beams? [5.7 mm]

Determine the deflection at pt C of the beam shown by: a. Conjugate Beam method b. Castigliano's 2nd theorem www 50 kN 90 kN B A C Fom 9 m- -9m El = constant E- 70 GPa I - 95 (106) mm

Question Two The beam ABC in Fig Q2 is supported on pin and roller supports at points A and C respectively. Determine the slope and deflection at point B of the beam shown by the 1. direct integration method 2. Moment-area method Take E = 70 GPa and I = 335x106 mm4. -2 m- B - 4 m Figure Q2 C 80 kN-m

Vertical rod CD of length L = 2 m, cross-sectional area A 150 mm2 %3D and modulus of elasticity E = 70 GPa supports a rigid beam AC of negligible weight, which, in turn, supports a uniformly distributed load over segment AB. When there is no load, the beam is horizontal. Determine wo (in kN/m) if the allowable deflection at A is 10 mm. 2 m B. WO TA 2 m D.

A IS AT THE FIXED SUPPORT point B is 6 meters from left support, point C is 9 meters from left support . D AT THE END

A) Using a convergence criterion of 0.001 in finding the location of the maximum deflection of the beam shown below. All answers must be in 4-decimal places. The moment M, occurs at point C of the beam. a.) What are the reactions at the supports? b.) What is the value of C1? c.) Give the value of C2. d.) What is the general moment equation of the beam? e.) What is the slope equation of the beam? f.) Determine the maximum deflection of the beam? w kN/m 12 kN/m M A В E 2 m 2 m 2 т 25 kN Note : Take the value the 'w' as equal to the last two digits of your student id. If the last two digits are zero or less than 10 then take 'w' = 10 kN/m. Take the value the 'M,' as equal to the last two digits of your student id. If the last two digits are zero or less than 10 then take 'M,'= 10 kN-m.

6. Given the beam loaded as shown, determine the deflection at the midspan. Use Conjugate Beam Method. 270 kN 45 kN/m A C 3 m 3 m- - 3 m El = constant 200 GPa I = 1665x106mm4 E %3D

The cantilever beam consists of a W530 × 74 structural steel wide-flange shape [E = 200 GPa; I = 410 × 106 mm4]. Use discontinuity functions to compute the deflection vC of the beam at C for the loading shown.Assume LAB = 3 m, LBC = 2.2 m, P = 39 kN, w = 23 kN/m.

Using Unit Load Method

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