Question A cantilever beam (length L) of rectangular cross-section supports an inclined load P at its free end as shown. Calculate the maximum tensile stress due to the load P. Let b-75 mm, h-150 mm, L = 1.4 m, P-800 N and 0-30°
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- During construction of a highway bridge, the main girders are cantilevered outward from one pier toward the next (see figure). Each girder has a cantilever length of 48 m and an I-shaped cross section with dimensions shown in the figure. The load on each girder (during construction) is assumed to be 9,5 kN/m, which includes the weight of the girder. Determine the maximum bending stress in a girder due to this load.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 simply supported wooden I-beam with a 12-ft span supports a distributed load of intensity q = 90 lb/ft over its length (see figure part a). The beam is constructed with a web of Douglas-fir plywood and flanges of pine glued to the web, as shown in the figure part b. The plywood is 3/8 in. thick: the flanges are 2 in, × 2 in, (actual size). The modulus of elasticity for the plywood is 1,600,000 psi and for the pine is 1,200,000 psL Calculate the maximum bending stresses in the pine flanges and in the plywood web. What is q, if allowable stresses are 1600 psi in the flanges and 1200 psi in the web?
- A fixed-end beam AB supports a uniform load of intensity q = 75 lb/ft acting over part of the span. Assume that EI = 300kip-ft2. Calculate the reactions at A and B. Find the maximum displacement and its location. Repeat part (a) if the distributed load is applied from A to B.A singly symmetric beam with a T-section (see figure) has cross-sectional dimensions b = 140 mm, a = 190, 8 mm, b. = 6,99 mm, and fc = 11,2 mm. Calculate the plastic modulus Z and the shape factor.Two wood beams, each of rectangular cross section (3.0 in. x 4.0 in., actual dimensions), are glued together to form a solid beam with dimensions 6.0 in. x 4.0 in. (sec figure). The beam is simply supported with a span of S ft. What is the maximum moment Mmaxthat may be applied at the left support if the allowable shear stress in the glued joint is 200 psi? (Include the effects of the beams own weight, assuming that the wood weighs 35 lb/ft3.) Repeat part (a) if Mmaxis based on allowable bending stress of 2500 psi.
- 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.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.Find support reactions at A and D and then calculate the axial force N. shear force 1 and bending moment 11 at mid-span of column BD. Let L = 4 m, q0 = 160N/m, P = 200N, and M0= 380 N .m.
- 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-7A simple beam with an overhang is subjected to d point load P = 6kN. If the maximum allowable deflect ion at point C is 0.5 mm, select the lightest W360 section from Table F-l{b) that can be used for the beam. Assume that L = 3 m and ignore the distributed weight of the beam.Segments A B and BCD of beam A BCD are pin connected at x = 4 m. The beam is supported by a sliding support at A and roller supports at C and D (see figure). A triangularly distributed load with peak intensity of SO N/m acts on EC. A concentrated moment is applied at joint D. (a) Find reactions at supports A, C, and D. (b) Find internal stress resultants N, Y, and Mat x = 5m. (c) Repeat parts (a) and (b) for die case of the roller support at C replaced by a linear spring of stiffness kr™ 200 kN/m (see figure).