h) the maximum bending stress in the CFRP. Enter your answer in MPa to 2 decima A glue-laminated timber beam is reinforced by carbon fiber reinforced plastic (CFRP) material bonded to itsbottom surface. The cross section of the composite beam is shown in figure below. The elastic modulus of thewood is E= 12 GPa and the elastic modulus of the CFRP is 112 GPa. The simply supported beam spans L = 7 mand carries a concentrated load P=3.3 kN at midspan, see figure below.L/2If b₁ = 88 mm and b₂ = 42 mm determine:BSL/2CFRP→b₂250 mm3 mm

For a simply supported beam with point load at its mid-span, maximum bending moment isSubstitute all…

Answered: the maximum bending stress in the CFRP

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Mechanical Engineering

the maximum bending stress in the CFRP

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter6: Stresses In Beams (advanced Topics)

Section: Chapter Questions

Problem 6.3.9P: A simple beam thai is IS ft long supports a uni¬form load of intensity a. The beam is constructed of...

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-14 A simply supported composite beam with a 3.6 m span supports a triangularly distributed load of peak intensity q0at mid-span (see figure part a). The beam is constructed of two wood joists, each 50 mm x 280 mm, fastened to two steel plates, one of dimensions 6 mm × 80 mm and the lower plate of dimensions 6 mm x 120mm (see figure part b). The modulus of elasticity for the wood is 11 GPa and for the steel is 210 GPa. If the allowable stresses are 7 MPa for the wood and 120 MPa for the steel, find the allowable peak load intensity q0maxwhen the beam is bent about the z axis. Neglect the weight of the beam.
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 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 wood beam in a historic theater is reinforced with two angle sections at the outside lower corners (see figure). If the allowable stress in the wood is 12 M Pa and that in the steel is 140 M Pa, what is ratio of the maximum permissible moments for the beam before and after reinforcement with the angle sections? See Appendix F Table F-5(b) for angle section properties. Assume that ew= 12 GPa and E3=210 GPa.
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?
The cross section of a sand wie h beam consisting of aluminum alloy faces and a foam core is shown in the figure. The width b of the beam is 8.0 in, the thickness I of the faces is 0.25 in., and the height hcof the core is 5.5 in. (total height h = 6.0 in). The moduli of elasticity are 10.5 × 106 psi for the aluminum faces and 12.000 psi for the foam core. A bending moment M = 40 kip-in. acts about the z axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams and (b) the approximate theory for sandwich beams.
A steel plate (called a cover ploie) having cross-sectional dimensions 6,0 in. × 0.5 in. is welded along the full length of the bottom flange of a W 12 × 50 wide-flange beam (sec figure, which shows the beam cross section). What is the percent increase in the smaller section modulus (as compared to the wide-flange beam alone)?
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 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 wood beam with cross-sectional dimensions 200 mm x 300 mm is reinforced on its sides by steel plates 12 mm thick (see figure). The moduli of elasticity for the steel and wood are E±= 190 GPa and Ew= 11 GPa, respectively. Also, the corresponding allowable stresses are eS= 110 MPa and ew = 7.5 MPa, (a) Calculate the maximum permissible bending moment Mmaxwhen the beam is bent about the- axis. Repeat part (a) if the beam is now bent about its y axis. Find the required thickness of the steel plates on the beam bent about the y axis so that Mmaxis the same for both beam orientations.
The cantilever beam AB shown in the figure is an S6 × 12.5 steel I-beam with E = 30 × 106 psi. The simple beam DE is a wood beam 4 in. x 12 in. (nominal dimensions) in cross section with E = 1.5 x 106 psi. A steel rod AC of diameter 0.25 in., length 10 ft, and E = 30 x 106 psi serves as a hanger joining the two beams. The hanger fits snugly between the beams before the uniform load is applied to beam DE. Determine the tensile force Fin the hanger and the maximum bending moments MABand MDEin the two beams due to the uniform load, which has an intensity q = 400 lb/ft. Hint: To aid in obtaining the maximum bending moment in beam DE, draw the shear-force and bending-moment diagrams.