For the beam in the figure that has as data: P = 24 kN, w = 12 kN /m and L = 8 m, El = cte. Applying the conjugate beam method, determine: a) the reaction of the simple support b) the displacement of the free end.
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- A r o lukI f/frm f «m t ub e of ou t sid e d ia met er ^ and a copper core of diameter dxare bonded to form a composite beam, as shown in the figure, (a) Derive formulas for the allowable bending moment M that can be carried by the beam based upon an allowable stress <7Ti in the titanium and an allowable stress (u in the copper (Assume that the moduli of elasticity for the titanium and copper are Er- and £Cu, respectively.) (b) If d1= 40 mm, d{= 36 mm, ETl= 120 GPa, ECu= 110 GPa, o-Ti = 840 MPa, and ctqj = 700 MPa, what is the maximum bending moment Ml (c) What new value of copper diameter dtwill result in a balanced design? (i.e., a balanced design is that in which titanium and copper reach allow- able stress values at the same time).A cantilever beam has a length L = 12 ft and a rectangular cross section (b = 16 in., h = 24 in.), A linearly varying distributed load with peak intensity q0acts on the beam, (a) Find peak intensity q0if the deflection at joint B is known to be 0.18 in. Assume that modulus E = 30,000 ksi. (b) Find the location and magnitude of the maximum rotation of the beam.A cantilever beam is subjected to a concentrated moment at B, The length of the beam L = 3 m and the height h = 600 mm. The longitudinal strain at the top of the beam is 0,0005 and the distance from the neutral surface to the bottom surface of the Iva m is 300 nun. Find the radius of curvature, the curvature, and the deflection of the beam at B.
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- A beam made up all woun equal leg angles is subjected to a bending moment M having its vector .u an angle (i) lo lire axis (see figure paria). (a) For the position shown in lire figure, determine lire orienlalion of lire neulral axis and calculate lire maximum tensile s'av-s ir, and maximum compressive stress (b) The two angles are now inverted and attached back-lo-back lo lorn, a lintel beam that supports two courses of brick facade i see figure part b). Find the new orientation of the neutral axis and calculate the maximum tensile slress r. a::d maximum compressive s'avsrr . in I he beam using 6 = 30° and M = 30 kip-in.A beam is constructed using two angle sections (L 102 × 76 × 6.4) arranged back to back, as shown in the figure. The beam is fixed al joint A and attached to an elastic support having a spring constant k = l750 kN/m al joint B. Assume only the beam is subjected to temperature increase AT = 45°C. Calculate the thermal stress developed in the beam and the displacement at point B. Assume that a = 12 X 10-6/?. Let E = 205 GPaA fixed-end beam AB carries point load P acting at point C. The beam has a rectangular cross section (b = 75 mm, h = 150 mm). Calculate the reactions of the beam and the displacement at point C. Assume that E = 190 GPa.