A circular cross-section Beam has a simple headstock from the ends, as shown in the figure, Q is uniform it is exposed to the effect of its radiated charge and the singular force P from the end of B. Lowest cross section of beam çalculate the maximum normal stress (Max) that occurs at the point.
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- 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 reinforced concrete beam (see figure) is acted on by a positive bending moment of M = 160 kN · m. Steel reinforcement consists of 4 bars of 28 mm diameter. The modulus of elasticity for the concrete is Ec= 25 GPa while that of the steel is Es= 200 GPa. Find the maximum stresses in steel and concrete. If allowable stresses for concrete and steel are T2= 9.2 MPa and t1= 135 MPa, respectively, what is the maximum permissible positive bending moment? What is the required area of steel reinforcement, A$ if a balanced condition must be achieved? What is the allowable positive bending moment? (Recall that in a balanced design, both steel and concrete reach allowable stress values simultaneously under the design moment.)A bimetallic beam used in a temperature-control switch consists of strips of aluminum and copper bonded together as shown in the figure, which is a cross-sectional view. The width of the beam is LO in,, and each strip has a thickness of 1/16 in. Under the action of a bending moment M = 12 lb-in, acting about the z axis, what are the maximum stresses aaand ecin the aluminum and copper, respectively? (Assume fA, = 10,5 x l0 psi and ecu= 16,8 × 106 psi,)
- A reinforced concrete T-beam (see figure) is acted on by a positive bending moment of M = 175 kip-ft. Steel reinforcement consists of four bars of 1.41-inch diameter. The modulus of elasticity for the concrete is Ec= 3000 ksi while that of the steel is £s = 29,000 ksi. Let b = 48 im, rf = 4 in., bw=15 in,, and d = 24 in, Find the maximum stresses in steel and concrete, If allowable stresses for concrete and steel are o"ac = 1400 psi and tr^ =18 ksi, respectively, what is the maximum permissible positive bending moment?A beam is constructed of two angle sections, each L5 x 3 x 1/2, that reinforce a 2 x g (actual dimensions) wood plank (see the cross section shown in the figure). The modulus of elasticity for the wood is £w = L2 X 106 psi and for the steel is Es= 30 x 106 psi. Find the allowable bending moment M3][cmfor the beam if the allowable stress in the wood is trv= 1100 psi and in the steel is 3 = 12,000 psi. Note: Disregard the weight of the beam, and see Table F-5(a) of Appendix F for the dimensions and properties of the angles.A reinforced concrete slab (see figure) is reinforced with 13-mm bars spaced 160 mm apart at d = 105 mm from the top of the slab. The modulus of elasticity for the concrete is Ec= 25 GPa, while that of the steel is £s = 200 G Pa. Assume that allowable stresses for concrete and steel arecrac = 9.2 MPa and us = 135 MPa. l()5 mm Find the maximum permissible positive bending moment for a l-m wide strip of the slab. What is the required area of steel reinforcement, A^ if a balanced condition must be achieved? What is the allowable positive bending moment? (Recall that in a balanced design, both steel and concrete reach allowable stress values simultaneously under the design moment.)
- A r o lukI f/frm f «m t ub e of ou t sid e d ia met er ^ and a copper core of diameter dxare bonded to form a composite beam, as shown in the figure, (a) Derive formulas for the allowable bending moment M that can be carried by the beam based upon an allowable stress <7Ti in the titanium and an allowable stress (u in the copper (Assume that the moduli of elasticity for the titanium and copper are Er- and £Cu, respectively.) (b) If d1= 40 mm, d{= 36 mm, ETl= 120 GPa, ECu= 110 GPa, o-Ti = 840 MPa, and ctqj = 700 MPa, what is the maximum bending moment Ml (c) What new value of copper diameter dtwill result in a balanced design? (i.e., a balanced design is that in which titanium and copper reach allow- able stress values at the same time).A composite beam consisting of fiberglass faces and a core of particle board has the cross section shown in the figure. The width of the beam is 2,0 in., the thickness of the faces is 0,10 in., and the thickness of the core is 0.50 in. The beam is subjected to a bending moment of 250 lb-in, acting about the - axis. Find the maximum bending stresses tr(and ctc in the faces and the core, respectively, if their respective moduli of elasticity are 4 x 106 psi and 1.5 x 106 psi.Two flat beams AB and CD, lying in horizontal planes, cross at right angles and jointly support a vertical load P at their midpoints (see figure). Before the load P is applied, the beams just touch each other. Both beams are made of the same material and have the same widths. Also, the ends of both beams are simply supported. The lengths of beams AB and CD are LABand LCD, respectively. What should be the ratio tABltCDof the thicknesses of the beams if all four reactions arc to be the same?
- 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.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 displacementThe cross section of a composite beam made of aluminum and steel is shown in the figure. The moduli of elasticity are TA= 75 GPa and Es= 200 GPa. Under the action of a bending moment that produces a maximum stress of 50 M Pa in the aluminum, what is the maximum stress xs in the steel? If the height of the beam remains at 120 mm and allowable stresses in steel and aluminum are defined as 94 M Pa and 40 M Pa, respectively, what heights h and h. arc required for aluminum and steel, respectively, so that both steel and aluminum reach their allowable stress values under the maximum moment?