A Simply Supported beam of 4 m span is in the form of hollow square bar (120x120 mm) as shown in Figure Q4 It carries a point load of 40 kN at the mid span. Draw the shear stress distribution at 1 m from the left support.
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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.Segments AB and BCD of beam ABCD are pin connected at x = 10 ft. The beam is supported by a pin support at A and roller supports at C and D; the roller at D is rotated by 30* from the x axis (see figure). A trapezoidal distributed load on BC varies in intensity from 5 lb/ft at B to 2.5 lb/ft at C. A concentrated moment is applied at joint A, and a 40-lb inclined load is applied at the mid-span or CD. (a) Find reactions at supports A, C, and D. (b) Find the resultant force in the pin connection at B. (c) Repeat parts (a) and (b) if a rotational spring(kr= 50 ft-lb/radian ) is added at A and the roller at C is removed.A solid circular pole is subjected to linearly varying distributed force with maximum intensity q0at the base and an axial compressive load P at the top (see figure). Find the required diameter d of the pole if the maximum allowable normal stress is 150 M Pa. Let q0= 6.5 kN/m, P = 70 kN, and L = 3 m.
- A wood beam with a rectangular cross section (see figure) is simply supported on a span of length L. The longitudinal axis of the beam is horizontal, and the cross section is tilted at an angle a. The load on the beam is a vertical uniform load of intensity q acting through the centroid C. Determine the orientation of the neutral axis and calculate the maximum tensile stress bmaxif PROBLEMS 6.4-2 and 6.4-3 b = 80 mm, b = 140 mm, L = 1,75 m, a — 22.5°, and q = 7.5 kN/m.Two pipe columns (AB, FC) are pin-connected to a rigid beam (BCD), as shown in the figure. Each pipe column has a modulus of E, but heights (L1or L2) and outer diameters (d1or different for each column. Assume the inner diameter of each column is 3/4 of outer diameter. Uniformly distributed downward load q = 2PIL is applied over a distance of 3L/4 along BC, and concentrated load PIA is applied downward at D. (a) Derive a formula for the displacementA retaining wall 6 ft high is constructed of horizontal wood planks 2.5 in. thick (actual dimension) that are supported by vertical wood piles of a 12 in, diameter (actual dimension), as shown in the figure. The lateral earth pressure is pt=125 lb/ft2 at the top of the wall and p2= 425 lb/ft2 at the bottom. Assuming that the allowable stress in the wood is 1175 psi, calculate the maximum permissible spacing s of the piles. Find the required diameter of the wood piles so that piles and planks (f = 2.5 in.) reach the allowable stress at the same time. Hint: Observe that the spacing of the piles may be governed by the load-carrying capacity of either the planks or the piles. Consider the piles to act as cantilever beams subjected to a trapezoidal distribution of load, and consider the planks to act as simple beams between the piles. To be on the safe side, assume that the pressure on the bottom plank is uniform and equal to the maximum pressure.
- An overhanging beam ABC has a guided support at A, a rectangular cross section, and supports an upward uniform load q = PtL over AB and a downward concentrated load P at the free end C {see figure). The span length from A to B is L, and the length of the overhang is L12. The cross section has a width of A and a height A. Point D is located midway between the supports at a distance d from the top face of the beam. Knowing that the maximum tensile stress (principal stress) at point Z> is tr, = 38 MPa, determine the magnitude of the load P. Data for the beam are L = 1.75 m, b = 50 mm, // = 220 mm, and d = 55 mm.Each girder of the lift bridge (sec figure) is 180 ft long and simply supported at the ends. The design load for each girder is a uniform load of intensity 1,6 kips/ft. The girders are fabricated by welding three steel plates to form an I-shaped cross section (see figure) having section modulus S = 3600 in3. What is the maximum bending stress rmaxin a girder due to the uniform load?A simple beam of span length 3.2 m carries a uniform load of intensity 48 kN/m, The cross section of the beam is a hollow box with wood flanges and steel side plates, as shown in the figure. The wood flanges are 75 mm x 100 mm in cross section, and the steel plates are 300 mm deep. What is the required thickness t of the steel plates if the allowable stresses are 120 M Pa for the steel and 6,5 M Pa for the wood? (Assume that the moduli of elasticity for the steel and wood are 210 GPa and 10 GPa, respectively, and disregard the weight of the beam.)
- A palm tree weighing 1000 lb is inclined at an angle of 60º (see figure). The weight of the tree may be resolved into two resultant forces: a force P1= 900 lb acting at a point 12 ft from the base and a force P2= 100 lb acting at the top of the tree, which is 30 ft long. The diameter at the base of the tree is 14 in. Calculate the maximum tensile and compressive stresses et, and ec, respectively, at the base of the tree due to its weight.A bridge girder A B on a simple span of length L = 14 m supports a distributed load of maximum intensity q at m id-span and minimum intensity q/2 at supports A and B that includes the weight of the girder (sec figure). The girder is constructed of three plates welded to form the cross section shown. Determine the maximum permissible load q based upon (a) an a I lowable bending stress tra]Um = 110 M Pa and (b) an allowable shear stress r ,. = 50 M Pa.A cantilever beam(Z, = 6 ft) with a rectangular cross section (/> = 3.5 in., h = 12 in.) supports an upward load P = 35 kips at its free end. (a) Find the state of stress ((7T, o^., and r in ksi) on a plane-stress element at L/2 that is i/ = 8 in. up from the bottom of the beam. Find the principal normal stresses and maximum shear stress. Show these stresses on sketches of properly oriented elements. (b) Repeat part (a) if an axial compressive centroidal load N = 40 kips is added at B