4.5-18 Beam ABCwith an overhang at one end supports a partial uniform load of intensity 12 kN/m and a concen- trated moment of magnitude 4 kNm at C (see figure). Draw the shear-force and bending-moment diagrams for this beam. 4 kN · m 12 kN/m А B 10 1.6 m -1.6 m- -1.6 m PROBLEM 4.5-18
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- A beam with a channel section is subjected to a bending moment M having its vector at an angle 8 to the 2 axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress tt and maximum compressive stress crc in the beam. Use a C 200 × 20.5 channel section with M = 0.75 kN - m and 0 = 20°.The beam ABC shown in the figure is simply supported at A and B and has an overhang from B to C Draw the shear-force and bending-moment diagrams for beam ABC. Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations.A beam with simple supports is subjected to a trapezoidally distributed load (see figure). The intensity of the load varies from 1.0 kN/m at support A to 2.5 kN/m at support B. Draw the shear-force and bending-moment diagrams for this beam. Assume that Mfl at B is zero. Find the required moment MQat B so that the maximum moment in the beam does not exceed 1.0 kN · m.
- A propped cantilever beam is subjected to two triangularly distributed loads, each with a peak load intensity equal to q0(see figure), lind the expressions for reactions at A and C using superposition. Plot shear and moment diagrams.-1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress t (obtained by dividing the shear force by the area of the web) and the ratio tmax/taver. The shear force Vweb/V carried in the web and the Vweb/V. Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-1 Dimensions of cross section: b = 6 in,, ï = 0.5 in., h = 12 in,, A, = 10.5 in., and V = 30 k.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.
- -1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^ The shear force carried in the web and the ratio K b/K. Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-2 Dimensions of cross section: b = 180 mm, v = 12 mm, h = 420 mm, i = 380 mm, and V = 125 kN.-1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^. The shear force i^/t^ carried in the web and the ratio V^tV. Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-6 Dimensions of cross section: b = 120 mm, a = 7 mm, h = 350 mm, hx= 330 mm, and K=60kN.A steel beam of I-section (see figure) is simply supported at the ends. Two equal and oppositely directed bending moments M0act at the ends of the beam, so the beam is in pure bending. The moments act in plane mmalwhich is oriented at an angle of to the x-y plane. Determine the orientation of the neutral axis and calculate the maximum tensile stress tarm, due to the moments MnData for the beam are S 200 x 21A section, M0= 4 kN m, and a = 24°. Noie: See Table F-2(b) of Appendix F for the dimensions and properties of the beam.
- Find expressions for shear force V and moment M at v = L/2 of beam AB in structure (a). Express V and M in terms of peak load intensity q0and beam length variable L. Repeat for structure (b) but find Fand M at m id-span of member BC.A propped cantilever beam with a length L = 4 m is subjected to a trapezoidal load with intensities q0= 10 kN/m and q1 = 15 kN/m. Find the reactions at A and B. Hint: The loading is the sum of uniform and triangular loads.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-7