The cantilever beam ABC has the rectangular cross section shown in the figure. Using E = 69 GPa, determine the maximum displacement of the beam.
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The cantilever beam ABC has the rectangular cross section shown in the figure. Using E = 69 GPa, determine the maximum displacement of the beam.
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- The 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.The cross section of a bimetallic strip is shown in the figure. Assuming that the moduli of elasticity for metals A and B are EA=168 GPa and EB= 90 GPa, respectively, determine the smaller of the two section moduli for the beam. (Recall that section modulus is equal to bending moment divided by maximum bending stress.) In which material does the maximum stress occur?A 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 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-7Two identical, simply supported beams AB and CD are placed so that they cross each other at their midpoints (sec figure). Before the uniform load is applied, the beams just touch each other at the crossing point. Determine the maximum bending moments (mab)max* and (MCD)max beams AB and CD, respectively, due to the uniform load if the intensity of the load is q = 6.4 kN/m and the length of each beam is L = 4 m.A tapered cantilever beam A B of length L has square cross sections and supports a concentrated load P at the free end (sec figure part a). The width and height of the beam vary linearly from kAat the free end to hBat the fixed end. Determine the distance.y from the free end A to the cross section of maximum bending stress if hE= 3h4, What is the magnitude ffœai of the maximum bending stress? What is the ratio of the maximum stress to the largest stress B at the support? Repeat part (a) if load P is now applied as a uniform load of intensity q = P/L over the entire beam, A is restrained by a roller support, and B is a sliding support (see figure part b).
- The cross section of an unbalanced wide-flange beam is shown in the figure. Derive the following formula for the distance /h from the centerline of one flange to the shear center S: h1t2b23ht1b13+t2b23 Also, check the formula for the special cases of a T-beam (b2= t2=0) and a balanced wide-flange beam (t2= ttand b2= ty).A tapered cantilever beam A B supports a concentrated load P at the free end (see figure). The cross sections of the beam are rectangular with constant width A, depth d Aat support A, and depth ds= ^dJ2 at the support. Thus, the depth d and moment of inertia / at distance x from the free end are, respectively, in which / 4 is the moment of inertia at end A of the beam. Determine the equation of the deflection curve and the deflection S 4at the free end of the beam due to the load P.A small dam of a height h = 6 ft is constructed of vertical wood beams AB, as shown in the figure. The wood beams, which have a thickness I = 2.5 in., are simply supported by horizontal steel beams at A and Ä Construct a graph showing the maximum bending stress tram in the wood beams versus the depth d of the water above the lower support at B. Plot the stress0mas(psi) as the ordinate and the depth d(ft) as the abscissa. Note: The weight density y of water equals 62.4 lb/ft3.
- .20 Determine the plastic moment Mpfor beam having the cross section shown in the figure ey=210 MPa.The tapered cantilever beam AB shown in the figure has a solid circular cross section. The diameters at the ends A and B are dAand dB= 2dA, respectively. Thus, the diameter d and moment of inertia / at distance v from the free end are, respectively, in which IAis the moment of inertia at end A of the beam. Determine the equation of the deflection curve and the deflection SAat the free end of the beam due to the load P.A beam with a channel section is subjected to a bending moment M having its vector at an angle 0 to the 2 axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress et and maximum compressive stress ecin the beam. Use the following data: C 8 × 11.5 section, M = 20 kip-in., tan0=l/3. See Table F-3(a) of Appendix F for the dimensions and properties of the channel section.