The beam shown has an second moment of area of 9,500,000 mm4 and a controlling section modulus of 80,500 mm³. If a maximum bending moment of +1507 Nm is applied to the beam, determine the maximum flexural stress produced in the beam cross section. Note: Give your answer in MPa
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- A C 200 x 17.1 channel section has an angle with equal legs attached as shown; the angle serves as a lintel beam. The combined steel section is subjected to a bending moment M having its vector directed along the z axis, as shown in the figure. The cent roi d C of the combined section is located at distances xtand ycfrom the centroid (C1) of the channel alone. Principal axes yl and yvare also shown in the figure and properties Ix1,Iy1and 0pare given. Find the orientation of the neutral axis and calculate the maximum tensile stress exand maximum compressive stress if the angle is an L 76 x 76 x 6.4 section and M = 3.5 kN - m. Use the following properties for principal axes for the combined section:/^, = 18.49 X 106 nrai4,/;| = 1.602 X 106 mm4, ep= 7.448*(CW),_r£ = 10.70 mm,andvf= 24.07 mm.The cross section of a rectangular beam having a width b and height h is shown in part a of the figure. For reasons unknown to the beam designer, it is planned to add structural projections of width b/9 and height d/9 the top and bottom of the beam (see part b of the figure). For what values of d is the bending-moment capacity of the beam increased? For what values is it decreased?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 simple beam ACE is constructed with square cross sections and a double taper (see figure). The depth of the beam at the supports is dAand at the midpoint is dc= 2d 4. Each half of the beam has length L. Thus, the depth and moment of inertia / at distance x from the left-hand end are, respectively, in which IAis the moment of inertia at end A of the beam. (These equations are valid for .x between 0 and L, that is, for the left-hand half of the beam.) Obtain equations for the slope and deflection of the left-hand half of the beam due to the uniform load. From the equations in part (a), obtain formulas for the angle of rotation 94at support A and the deflection Scat the midpoint.A rectangular bar having width twice the depth is used as a beam. The beam is made of mild steel material having elastic modulus of 2.1 x 105 N/mm? and it undergoes bending by external load which makes radius of curvature of 150 m. If the allowable bending stress in the beam is to be limited to 100 MN/m. find the cross section of the beam.Draw the Shear Force and Bending Moment Diagram for the loaded simply supported beam shown below. Ignore the self-weight of the beam. Also, Find the maximum bending stress in the beam, if its cross section is rectangular, that it is 15 cm wide and 20 cm deep. Also, determine the stress in a fiber located at 6 cm & 10 cm from the top of the beam.
- A beam of rectangular section of 12 cm × 20 cm is simply supported over a span of 12 m. It is acted upon by a load of 80 kN at the mid span. Determine the maximum bending stress induced in thr beam.A beam having a tee-shaped cross section is subjected to equal 13 kN-m bending moments, as shown. Assume bf = 95 mm, tf = 25 mm, d = 165 mm, tw = 40 mm. The cross-sectional dimensions of the beam are also shown. Determine(a) the centroid location (measured upward from the bottom), the moment of inertia about the z axis, and the controlling section modulus about the z axis.(b) the bending stress at point H (positive if tensile and negative if compressive).(c) the maximum bending stress (positive if tensile and negative if compressive) produced in the cross section.An I section symmetrical beamhas 200mm wide flange and overall depth of 500mm. Each flange is 25mm thickand the web is 20mm thick. Determine the maximum bending moment that should be imposed in the sectionif the tensile or the compressive stressis not to exceed 40MN/m^2 and what percentage of the moment is resisted by flange or web?
- The steel beam has the cross section shown. The beam length is L = 6.7 m, and the cross-sectional dimensions are d = 390 mm, bf = 205 mm, tf = 14 mm, and tw = 10 mm. Calculate the largest intensity of distributed load w0 that can be supported by this beam if the allowable bending stress is 230 MPa.A 6 ft long 2” x 12” beam is subjected to a uniform (edge-to-edge) distributed load of 1500 lbs per linear foot. The material has a Young's Modulus E=2,000,000psi. If the allowed bending stress is 2000 psi, the allowed deflection is L/360 and the allowed shear stress is 250 psi: Is the beam safe in bending? Is the beam safe in deflection for L/360, ( deflDIST = (5 w L4)/(384 E I)? Is the beam safe in shear?Calculate the maximum def lection δmaxof a uniformly loaded simple beam if the spanlength L = 2.0 m, the intensity of the uniform loadq =2.0 kN/m, and the maximum bending stressσ = 60 MPa.The cross section of the beam is square, and thematerial is aluminum having modulus of elasticityE = 70 GPa.