Calculate the shear force and the maximum bending moment of beams using for the construction bridge and building. An Encastre /Built-in beam has a span of 3 m and carries the loading system shown in figure 1. 40kN 30KN/m -1.8m -1.2m Figure 1: Encastre / Built-in beam
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- A pontoon bridge (see figure) is constructed of two longitudinal wood beams, known as bulks, that span between adjacent pontoons and support the transverse floor beams, which arc called chesses. For purposes of design, assume that a uniform floor load of 7.5 kPa acts over the chesses. (This load includes an allowance for the weights of the chesses and balks.) Also, assume that the chesses are 2.5 m long and that the balks are simply supported with a span of 3.0 m. The allowable bending stress in the wood is 15 MPa. If the balks have a square cross section, what is their minimum required width b^l Repeat part (a) if the balk width is 1.5 b and the balk depth is b; compare the cross-sectional areas of the two designs.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 hollow box beam is constructed with webs of Douglas-fir plywood and flanges of pine, as shown in the figure in a cross-sectional view. The plywood is 1 in. thick and 12 in. wide; the flanges are 2 in. × 4 in. (nominal size). The modulus of elasticity for the plywood is 1,800,000 psi and for the pine is 1,400,000 psi. If the allowable stresses are 2000 psi for the plywood and 1750 psi for the pine, find the allowable bending moment Mmaxwhen the beam is bent about the z axis. Repeat part (a) if the beam is now bent about its y-axis.
- A simple beam with a W 10 x 30 wide-flange cross section supports a uniform load of intensity q = 3.0 kips/ft on a span of length L = 12 ft (sec figure). The dimensions of the cross section are q = 10.5 in., b = 5.81 in., t1= 0.510 in., and fw = 0.300 in. Calculate the maximum shear stress tjuly on cross section A—A located at distance d = 2.5 ft from the end of the beam. Calculate the shear stress rat point Bon the cross section. Point B is located at a distance a = 1.5 in. from the edge of the lower flange.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.A weight W = 4000 lb falls through a height h = 0.5 in, onto the midpoint of a simple beam of length L = 10 ft (see figure). Assuming that the allowable bending stress in the beam is = 18,000 psi and E = 30 x 10* psi, select the lightest wide-flange beam listed in Table F-l(a) in Appendix F that will be satisfactory.
- The hollow box beam shown in the figure is subjected to a bending moment M of such magnitude that the flanges yield but the webs remain linearly elastic. (a) Calculate the magnitude of the moment M if the dimensions of the cross section are A = 15 in., A] = 12.75 in., h = 9 in., and ey =7.5 in. Also, the yield stress is eY = 33 ksi. (b) What percent of the moment M is produced by the elastic core?Derive the formula for the bending stress of a beam with a rectangular cross section and triangular cross secrion. Thank youFigure 3 below shows a 16 m length of beam with a pinned support at A and roller support at C. The beam carries a uniformly distributed load (UDL) of 20 kN/m across section A to B and a transverse uniformly distributed load (UDL) of 10 kN/m across section D to E. i) Sketch the Free Body Diagram (FBD) of the beam then identify the reaction force. ii) Analyze the shear force, V and sketch Shear Force Diagram (SFD). ii) Analyze the bending moment, M and sketch the Bending Moment Diagram (BMD). 20 kN/m 10 kN/m C В D →* 3m 5 m 5 m 3 m Figure 3
- Activity 1 Calculate the shear force and the maximum bending moment of beams using for the construction bridge and building. An Encastre /Built-in beam has a span of 3 m and carries the loading system shown in figure 1 (a). 40KN 30kN/m 1.8m -1.2m Figure 1(a): Encastre / Built-in In addition, you should be able to calculate the shear force and the maximum bending moment of a cantilever beam, with a hollow cross-section of Dout: 0.2 m, wall thickness of 0.02 m, and the length of 3 (m). The beam is subjected to a point load of 50 kN at its free end as shown in Figure 1 (b). Dout 50KN 3m Figure 1(b): Cantilever beamHelp me plsThe figure below shows two solid homogenous rectangular beam sections with (breadth x depth) dimensions in two different orientations as follows: Beam Section Orientation A (t mm x 2t mm); and Beam Section Orientation B (2t mm x tmm). Both beams sag when subjected to the same loading and support conditions resulting in compressive stresses above the centroid line (neutral axis). Which statement accurately describes the relative maximum compressive stress (ocompression) between these beam section orientations? O a. O b. Oc tmm 2 mm Beam Section Orientation A 2tmm 7 mm Beam Section Orientation B Maximum compressive stress (compression) in orientation B is greater than orientation A by a factor of 2. Maximum compressive stress (ocompression) in orientation A is greater than orientation B by a factor of 4. Maximum compressive stress (compression) in orientation B is greater than orientation A by a factor of 4. O d. Maximum compressive stress (ocompression) in orientation A is greater than…