Problem A timber beam of rectangular section is to support a load of 20 kN uniformly distributed over a span of 3.6 m when beam is simply supported. If the depth of section is to be twice the breadth, and the stress in the timber is not to exceed 7 NImm², find the dimensions of the cross-section.
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- A simply supported beam of span 3.0 m has a cross-section 120 mm × 180 mm. If the permissible stress in the material of the beam is 10 N/mm^2, determine maximum udl it can carry.A retaining wall 6 ft high is constructed ofhorizontal wood planks 2.5 in. thick (actual dimension)that are supported by vertical wood piles of a12 in. diameter (actual dimension), as shown in thefigure. The lateral earth pressure is p1 125 lb/ft2at the top of the wall and p2 =425 lb/ft2 at the bottom.(a) Assuming that the allowable stress in the woodis 1175 psi, calculate the maximum permissiblespacing s of the piles.(b) Find the required diameter of the wood pilesso that piles and planks (t = 2.5 in.) reach theallowable stress at the same time.Hint: Observe that the spacing of the piles may begoverned by the load-carrying capacity of either theplanks or the piles. Consider the piles to act as cantileverbeams subjected to a trapezoidal distribution ofload, and consider the planks to act as simple beams between the piles. To be on the safe side, assume thatthe pressure on the bottom plank is uniform andequal to the maximum pressure.A pontoon bridge (see figure) is constructedof two longitudinal wood beams, known as balks,that span between adjacent pontoons and supportthe transverse floor beams, which are called chesses.For purposes of design, assume that a uniform floorload of 7.5 kPa acts over the chesses. (This loadincludes an allowance for the weights of the chessesand balks.) Also, assume that the chesses are 2.5 m long and that the balks are simply supported with aspan of 3.0 m. The allowable bending stress in thewood is 15 MPa.(a) If the balks have a square cross section, what istheir minimum required width bmin?(b) Repeat part (a) if the balk width is 1.5 b andthe balk depth is b; compare the cross-sectionalareas of the two designs.
- A small balcony constructed of wood issupported by three identical cantilever beams (seefigure). Each beam has length L1 = 2.1m, width b,and height h = 4b/3. The dimensions of the balconyfloor are L1 XL2, where L2 = 2.5 m. The designload is 5.5 kPa acting over the entire floor area.(This load accounts for all loads except the weightsof the cantilever beams, which have a weight densityΥ = 5.5 kN/m3.) The allowable bending stress in thecantilevers is 15 MPa.Assuming that the middle cantilever supports50% of the load and each outer cantilever supports25% of the load, determine the required dimensions band h.A beam of rectangular cross-section is 64 mm broad, 100 mm deep, and 1.6 m long. It is simply supported at each end and carries a concentrated load of 10 kN at its mid-length. Neglecting the weight of the beam, find the maximum stress in the material.A simply supported beam is subjected to alinearly varying distributed load q(x) =(x/L)q0 withmaximum intensity q0 at B. The beam has a lengthL = 4 m and rectangular cross section with a widthof 200 mm and height of 300 mm. Determine themaximum permissible value for the maximum intensity,q0, if the allowable normal stresses in tension andcompression are 120 MPa.
- The cross section of a reinforced concrete beam is shown below. It has a modular ratio of 15. If the allowable compressive stress in the concrete is 6 MPa and the allowable tensile stress in the steel is 120 MPa, determine diameter of the three reinforcing steel rods to make the beam an economic section.In a 2.5 cantilevered I-beam, 2500 kg weight is applied at 0.75 meter from the free end. If the allowable stress in beam is 120 Mpa, determine the section modulus and The base and height of the beam if the base is 75% of its height mm.An electric power transmission pole is 12 m above ground level and embedded 2 m into the ground. The butt diameter is 450 mm and the tip diameter (the top of the pole) is 320 mm. The weight of the pole, cross arms, and wires is 33 kN. Assuming the pole transmits the load as a point load, find the change in vertical stress in kPa at 1m depth.
- a rectangular beam with a span of 20ft is simply supported at both ends. The maximum flexural stress for the beam is 1200 psi and the dimensions of its cross-section are: b=4 in and h=10 in. If the beam is to be loaded at mid-span with a concentrated load of 2000lbs, will the beam collapse?A floor system in a small building consistsof wood planks supported by 2-in. (nominal width)joists spaced at distance s and measured from centerto center (see figure). The span length L of eachjoist is 12 ft, the spacing s of the joists is 16 in., andthe allowable bending stress in the wood is 1250 psi.The uniform floor load is 120 lb/ft2, which includesan allowance for the weight of the floor system itself.(a) Calculate the required section modulus S for thejoists, and then select a suitable joist size (surfacedlumber) from Appendix G, assuming thateach joist may be represented as a simple beamcarrying a uniform load.(b) What is the maximum floor load that can beapplied to your final beam selection in part (a)?Problem 3 only, solve carefully, include the units in every step and draw the diagram. Thanks! In a 2.5 m cantilevered I-beam, 2500 kg weight is applied at 0.75 meter from the free end. If the allowable stress inbeam is 120 Mpa, determine theA. section modulus, in3 B. The base and height of the beam if the base is 75% of its height, mm