А M H B W Figure-2
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- . A cantilever beam (width b = 3 in. and depth h = 6 in,) has a length L = 5 ft and is subjected to a point load P and a concentrated moment M = 20 kip-ft at end B. If normal stress trx= 0 at point C, located 0.5 in. below the top of the beam and 1 ft to the right of point Atfind point load P. Also show the complete state of plane stress on the element at point C.The Z-section of Example D-7 is subjected to M = 5 kN · m, as shown. Determine the orientation of the neutral axis and calculate the maximum tensile stress c1and maximum compressive stress ocin the beam. Use the following numerical data: height; = 200 mm, width ft = 90 mm, constant thickness a = 15 mm, and B = 19.2e. Use = 32.6 × 106 mm4 and I2= 2.4 × 10e mm4 from Example D-7The cross section of a steel beam is shown in the figure. This beam is subjected to a bending moment M having its vector at an angle 8 to the - axis. Determine the orientation of the neutral axis and calculate the maximum tensile stress tiand maximum compressive stress tcin the beam. Assume that e = 22.5° and M = 4.5 kN · m. Use cross-sectional properties Ix=93.14 × 106 mm4, Iy= 152.7 X 10e mm4, and 9 = 27.3º.
- A canti lever beam A B of a n isosceles t rapezoi-dal cross section has a length L = 0.8 m, dimensions bx= 80 mm and b2= 90 mm, and height h = 110 mm (see figure). The beam is made of brass weighing 85 kN/m3. Determine the maximum tensile stress asand maximum compressive stressA beam supporting a uniform load of intensity q throughout its length rests on pistons at points A, C and B (sec figure). The cylinders are filled with oil and are connected by a tube so that the oil pressure on each piston is the same. The pistons at A and B have diameter d1and the piston at C has diameter D2. (a) Determine the ratio of d2to d1so that the largest bending moment in the beam is as small as possible. Under these optimum conditions, what is the largest bending moment Mmaxin the beam? What is the difference in elevation between point C and the end supports?The cross section of a steel beam is constructed of a W 18 × 71 wide-flange section with a 6 in. × 1/2 in, cover plate welded to the top flange and a C 10 × 30 channel section welded to the bottom flange. This beam is subjected to a bending moment M having its vector at an angle tc to the - axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress oxand maximum compressive stress tcin the beam. Assume that S = 30e and M = 75 kip-in. Note: The cross-sectional properties of this beam were computed in Examples D-2 and D-5.
- 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 beam ABC with an overhang from B to C is constructed of a C 10 × 30 channel section with flanges facing upward (sec figure). The beam supports its own weight (30 lb/ft) plus a triangular load of maximum intensity g0 acting on the overhang. The allowable stresses in tension and compression arc IS ksi and 12 ksi, respectively. Determine the allowable triangular load intensity allow if tne distance L equals 4 ft. What is the allowable triangular load intensity fallow ^tnc Dcam is rotated 180e about its longitudinal centroidal axis so that the flanges are downward?A beam with a T-section is supported and loaded as shown in the figure. The cross section has width b = 2 1/2 in., height c = 3 in., and thickness t = 3/8 in. Determine the maximum tensile and compressive stresses in the beam. If the allowable stresses in tension and compression are 18 ksi and 12 ksi, respectively, what is the required depth h of the beam? Assume that thickness t remains at 3/8 in. and that flange width/) = 2.5 in. Find the new values of loads P and q so that the allowable tension (18 ksi) and compression (12 ksi) stresses are reached simultaneously for the beam. Use the beam cross section in part (a) (see figure) and assume that Lh and L3are unchanged.
- An aluminum pole for a street light weighs 4600 N and supports an arm that weighs 660 N (see figure). The center of gravity of the arm is 1.2 m from the axis of the pole, A wind force of 300 N also acts in the (y) direction at 9 m above the base. The outside diameter of the pole (at its base) is 225 mm, and its thickness is 18 mm. Determine the maximum tensile and compressive stresses o, and e1., respectively, in the pole (at its base) due to the weights and the wind force.A simply supported wide-flange beam of span length L carries a vertical concentrated load P acting through the centroid Cat the midpoint of the span (see figure). The beam is attached to supports inclined at an angle « to the horizontal. Determine the orientation of the neutral axis and calculate the maximum stresses at the outside corners of the cross section (points A, B. ZX and E) due to the load P. Data for the beam are W 250 x 44,8 section, L = 3.5 m, P = 18 kN, and a = 26,57 Note: See Table F-l(b) of Appendix F for the dimensions and properties of the beam.A cantilever wood beam with a width b = 100 mm and depth h = 150 mm has a length L = 2 m and is subjected to point load P at mid-span and uniform load q = 15 N/m. (a) If the normal stress trx= 0 at point C, located 120 mm below the top of the beam at the fixed support A, calculate the point load P, Also show the complete state of plane stress on the element at point C (b) Repeat Part a if er = 220 kPa. Assume that element C is a sufficient distance from support A so that stress concentration effects are negligible.