The magnitude of the maximum deflection is
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- Determine the longitudinal stiffness of a beam of length 1 m, area of cross-section of 3 x 10^-4 m^2, Young’s modulus of elasticity of 200 GPa.A fixed beam AB, 5 m long, is carrying a point load at its centre. The moment of inertia of the beam is 60 x 106 mm4 and modulus of elasticity for beam material is 2.2 x 105 N/mm2. End moments are taken to be 40 kN-m. The load at the centre isElasticity modulus E, for ACB beam with inertia I; a- Find the elastic curve equation by the singularity method. b- Find the reaction forces at Point A. c- Find the reaction force at Point B.
- Using Castigliano’s Theorem, determine the deflection equation for the cantilever beam shown below and evaluate the deflections at point B and point C.A cantilever beam has a length L =12 ft anda rectangular cross section (b = 16 in., h = 24 in.). Alinearly varying distributed load with peak intensityq0 acts on the beam.(a) Find peak intensity q0 if the deflection at joint Bis known to be 0.18 in. Assume that modulusE = 30,000 ksi.(b) Find the location and magnitude of the maximumrotation of the beam.A fixed-end beam is subjected to a pointload at mid-span. The beam has a rectangular crosssection (assume that the h/b ratio is 2) and is made ofwood (E =11GPa).(a) Find height h of the cross section if the maximumdisplacement of the beam is 2 mm.(b) Calculate the displacement of the beam at theinflection points.
- Find the slope and deflection equations for the beam shown. Determine thevertical deflection of point C. Consider P = 120 kN, l = 5m, a = 80 cm. EI = constant. Method of Double IntegrationThe cantilever beam AB of uniform cross section and length of 4 m is subjected to the loading of 40 kN at free end and 30 kN at a distance of 2 m from free end. The modulus of elasticity is 200 GPa and inertia is 28.8 x 10^6 mm^4. Calculate the total diflection of the beam at free end.The section modulus for the beam of hollow circular cross section of outer and inner diameters as 70mm and 40 mm respectively, is ______________ mm3. The section modulus (unit is in mm3)= ______________ Answer
- Find the shear and bending moment diagram using Moment DistributionMethod (MDM) for the second degree indeterminate beam where EI is constant.: A simple beam of length L has a clockwise moment M at the left support and half of that moment of the same direction at the right support.Which of the following gives the rotation at the left support and at the right support?Which of the following gives the deflection at midspan?A Cantilever beam of dimension 10 m x 45 mm x 65 mm. It carries a uniformly distributed load of 550 kN/m for entire span. Determine (a) Maximum stress due to bending and (b) Young’s modulus of the material used for the beam, if it deflects 2 m maximum at the free end of the span. Also find the maximum slope of the beam. Moment of inertia of the cross section of the beam in m4 = ______________ Young's modulus of the beam material in GPa is = ___________ Maximum bending stress due to bending in MPa is = _________ The slope at the supports of beam in radians is = ___________