Materials for Civil and Construction Engineers (4th Edition)
4th Edition
ISBN: 9780134320533
Author: Michael S. Mamlouk, John P. Zaniewski
Publisher: PEARSON
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Chapter 11, Problem 11.22QP
To determine
The volume fraction of the fibers and matrix needed.
The modulus of elasticity of the composite.
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A circular FRP composite rod with continuous and aligned fibers has a 3 in. diameter. The rod is simply supported with a span of 4 ft and is subjected to three-point bending with a 270 lb center load.
a. If the maximum allowable center deflection cannot exceed 0.02 in., what is the minimum modulus of the composite in order to meet this requirement?
b. If the FRP has a modulus as obtained in Part a and the moduli of the matrix and the fibers are 0.5 × 10" psi and 20 × 10* psi, respectively. what is minimum percent of fibers that meets this requirement?
An aligned and continuous fiber reinforced composite consists of fibers with an elastic modulus of 42 * 106 psi and a matrix with an elastic modulus of 0.5 * 106 psi. If the fibers are required to carry 92% of the total load in the longitudinal direction (isostrain condition), determine the volume fraction of the fibers and matrix needed to accomplish this task. Also, determine the composite modulus of elasticity for this case.
Chapter 11 Solutions
Materials for Civil and Construction Engineers (4th Edition)
Ch. 11 - Prob. 11.1QPCh. 11 - Prob. 11.2QPCh. 11 - Prob. 11.3QPCh. 11 - Prob. 11.4QPCh. 11 - Prob. 11.5QPCh. 11 - Prob. 11.6QPCh. 11 - Prob. 11.7QPCh. 11 - Prob. 11.8QPCh. 11 - Prob. 11.9QPCh. 11 - What are the functions of aggregate used in...
Ch. 11 - Prob. 11.11QPCh. 11 - Prob. 11.12QPCh. 11 - What are the benefits of adding dispersed steel...Ch. 11 - Getting measurements from Figure 11.20, determine...Ch. 11 - Three 6 in. 12 in. concrete cylinders with...Ch. 11 - Prob. 11.16QPCh. 11 - Prob. 11.17QPCh. 11 - Prob. 11.18QPCh. 11 - Prob. 11.19QPCh. 11 - Prob. 11.20QPCh. 11 - Prob. 11.21QPCh. 11 - Prob. 11.22QPCh. 11 - Prob. 11.23QPCh. 11 - Prob. 11.24QPCh. 11 - Prob. 11.25QPCh. 11 - Prob. 11.26QPCh. 11 - Prob. 11.27QPCh. 11 - Prob. 11.28QPCh. 11 - Prob. 11.29QPCh. 11 - Prob. 11.30QPCh. 11 - A circular FRP composite rod with continuous and...
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- In Example Problem 12.1, a uniaxial composite material is made into a circular rod Vbith a 1.27-cm diameter from 70 volume percent continuous carbon fibers and 30 volume percent epoxy. The rod is subject to an axial force of 100,000 N. The composite matcrial in Example Problem 12.1 is to be replaced with a less expensive composite made of 70 volume percent continuous E-glass fibers and 30 volume percent epoxy. The elastic moduli are 5 GPa for the epoxy resin and 72.4 GPa fos the E-glass. (a) Compare the elastic modulus, composite strain, fiber and matrix stresses, and density of this composite with the carbon epoxy composite in Example Problem 12.1. Usc the density of UHM carbon, and assume the density of the epoxy is 1.2g/cm3 . (b) Can both the E-glass fiber and matrix withstand the applied force?arrow_forwardQ: For a continuous and oriented fiber-reinforced composite, the moduli of elasticity in the longitudinal and transverse directions are 19.7 GPa and 3.66 GPa, respectively. A) If the volume fraction of fibers is 0.25, determine the moduli of elasticity of fiber and matrix phases. B) If the cross-sectional area is 200 mm? and a stress of 40 MPa is applied in this longitudinal direction, compute the magnitude of the load carried by each of the fiber and matrix phases. C) Determine the strain that is sustained by each phase when the stress in part (b) is applied.arrow_forwardAn aligned and continuous fiber reinforced composite consists of fiberswith an elastic modulus of 290 GPa and a matrix with an elastic modulus of3.5 GPa. If the fibers are required to carry 92% of the total load in the longitudinal direction (isostrain condition), determine the volume fraction of the fibers and matrix needed to accomplish this task. Also, determine the composite modulus of elasticity for this case.arrow_forward
- An aligned and continuous fiber reinforced composite consists of fibers with an elastic modulus of 255 GPa and a matrix with an elastic modulus of 2.7 GPa. If the fibers are required to carry 98% of the total load in the longitudinal direction (isostrain condition), determine the volume fraction of the fibers and matrix needed to accomplish this task. Also, determine the composite modulus of elasticity for this case.arrow_forwardA circular FRP composite rod with continuous and aligned fibers has a3 in. diameter. The rod is simply supported with a span of 4 ft and is subjected to three-point bending with a 270 lb center load.a. If the maximum allowable center deflection cannot exceed 0.02 in.,what is the minimum modulus of the composite in order to meet this requirement?b. If the FRP has a modulus as obtained in Part a and the moduli of the matrix and the fibers are 0.5 * 106 psi and 20 * 106 psi, respectively, what is minimum percent of fibers that meets this requirement?arrow_forwardFor a continuous and oriented fiber-reinforced composite, the moduli of elasticity in the longitudinal and transverse directions are 19.7 and 3.66 GPa (2.8x10 and 5.3x 105 psi), respectively. If the volume fraction of fibers is 0.42, determine the moduli of elasticity of fiber and matrix phases. Em- E₁= i GPa GPaarrow_forward
- Q2: A composite component consists of a glass fiber and an epoxy matrix. The glass fiber weight fraction is triple of the epoxy weight fraction. Use the given properties of epoxy and glass to determine: 1. The composite axial modulus, transverse modulus, major Poisson's ratio, and in- plane shear modulus. 2. If the total load is 24 kN and the applied stress is 60 MPa in this axial direction, compute the cross-sectional area of the composite and the magnitude of the load carried by each of the fiber and matrix phases. Given: Glass p, 2.5 g/cm³. Ey-E 80 GPa. v 0.2, G 38 GPa epoxy Pm-1.2 g/cm', E-, E- 3.5 GPa, vy= 0.3, G= 1.35 GPaarrow_forwardQ6) How does moisture impact tension and compression strength in composites?arrow_forwardA fiber-reinforced polymer composite under isostrain condition consists of 35%fibers and 65% polymer by volume. The moduli of elasticity of the fibers and thepolymer are 260 GPa and 3.4 GPa, respectively, and the Poisson’s ratios of thefibers and the polymer are 0.25 and 0.41, respectively. Calculate the following:a. modulus of elasticity of the composite.b. percentage of load carried by the fibersc. Poisson’s ratio of the compositearrow_forward
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