10. The slope and deflection at a section in a loaded beam can be found out...
(a). A rectangular cross section at a location along a beam in bending is acted upon by a bending moment and a shear force. The cross section is \(120 \mathrm{~mm}\) wide, \(300 \mathrm{~mm}\) deep and is orientated such that it is in bending about its major axis of bending. The magnitudes of the bending moment and shear force are \(315 \mathrm{kNm}\) and \(240 \mathrm{kN}\) respectively. Determine the maximum bending and shear stresses on the cross section. Plot the bending and...
5. Determine the mid-span short-term deflection of a simply supported beam with the section shown in Figure Q5. Design data: Concrete strength: fcu 30 MPa. Area of tensile steel reinforcement: As 1500 mm Area of compressive steel reinforcement: A,-1500 mm2 Instantaneous static modulus of elasticity of concrete = 25GPa. Span -8.0 m Loading: Dead load 5.0 kN/m (uniformly distributed load); Live load 5.0 kN/m (uniformly distributed load) (Hint: the height of neutral axis of the mid-span section under the service...
1.A cantilever AD is subjected to a pure moment wa at B and uniformly distributed load of intensity w along AB and BC and as shown in Figure 1. The beam has constant EI. Ignore the weight of the beanm (a)Determine the reaction forces at the fixed end D. (6 marks) (b) Express the elastic curve of the beam in terms of EI, w, a and x. (14 marks) (c)Determine the allowable intensity w if the deflection at A is...
In Appendix C, see the simply supported beam with a uniformly distributed load. Be careful with units and the sign convention. For this calculation, the overhung part of the beam from C to D can be ignored, and the beam is treated as a simply supported beam of length 2L1. Be careful with units and the sign convention. The simply supported beam consists of a W530 × 66 structural steel wide-flange shape [ E = 200 GPa; I = 351...
Strength of Materials IV 9.2-5 The defiuction curve for a cantilever beam AB (see fgure) is given b 120LEI Describe the load acting on the beam. 2 .3-6 Calculate the maximum deflection dma of a uniformly loaded simple beam if the span length L 5 2.0 m, the intensity of the uniform load g 5 2.0 kN/m, and the maximum bending stress s 5 60 MPa. rn X The cross section of the beam is square, and the material is...
A simply supported wood beam of rectangular cross section and span length 2 m carries a uniformly distributed load of intensity 9 = 1 kN/m as shown. Calculate the maximum bending stress and the maximum shear stress in the beam.
1.2 (20 Marks) A beam of rectangular cross section (width b and height h) supports a uniformly distributed load along its entire length L. The allowable stresses in bending and shear are all and Tallow, respectively. a) If the beam is simply supported, what is the span length Lo below which the shear stress governs the allowable load and above which the bending stress governs? b) If the beam is supported as a cantilever, what is the length Lo below...
(2) A simply supported beam of flexural rigidity El carries a constant uniformly distributed load of intensity p per unit length as shown Figure 2 below. Assume the deflection shape to be a polynomial in x, and is given by v (x) = a., + as+ a2 x, where ao, a.呙are constants to be determined. (a) State the boundary conditions for the deflection equation. Using the boundary conditions stated in (a) and the Rayleigh-Ritz method, determine (b) the constants a,...
3. Determine the shape of the deflection curve of a uniform horizontal beam of length L and weight per unit length w that is fixed (horizontally) at the right end a1 and simply supported at the left end z = 0. 3. Determine the shape of the deflection curve of a uniform horizontal beam of length L and weight per unit length w that is fixed (horizontally) at the right end a1 and simply supported at the left end z...
A simply supported wood beam AB with span length L = 6 m carries a trapezoidal distributed load of intensity q = 4 kN/m at the left end and q/2 at the right end. Calculate the maximum bending stress Omax due to the load if the beam has a rectangular cross section with width b = 150 mm and height h = 250 mm.