Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
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Chapter 12, Problem 12.15P
To determine
The crack length produces fracture to composite.
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PROBLEM 6.56
50 mm
A steel bar and an aluminum bar are bonded together as shown to form a
composite beam. Knowing that the vertical shear in the beam is 18 kN and that
the modulus of elasticity is 200 GPa for the steel and 73 GPa for the aluminum,
determine (a) the average stress at the bonded surface, (b) the maximum stress
Aluminum
25 mm
Steel
in the beam.
36 mm
The stress-strain diagram of a reinforcement steel having a cross-sectional diameter of 12 mmdiameter and 100 mm gage length is determined after its tensile strength test as follows. Based on the stressstrain diagram determine the followings properties of the material (Poisson’s ratio of the material is 0.32) :
d) Resiliencee) Shear modulusf) Bulk modulusg) Ductility as described bypercent change in length
The stress value in reinforcement at the commencement of first crack in concrete is N/mm².
(Assume modulus of elasticity of steel as 216 GPa)
Chapter 12 Solutions
Materials Science And Engineering Properties
Ch. 12 - Prob. 1CQCh. 12 - Prob. 2CQCh. 12 - Prob. 3CQCh. 12 - Prob. 4CQCh. 12 - Prob. 5CQCh. 12 - Prob. 6CQCh. 12 - Prob. 7CQCh. 12 - Prob. 8CQCh. 12 - Composite _________ is produced by laying fibers...Ch. 12 - Prob. 10CQ
Ch. 12 - Prob. 11CQCh. 12 - Prob. 12CQCh. 12 - Prob. 13CQCh. 12 - Prob. 14CQCh. 12 - Prob. 15CQCh. 12 - Prob. 16CQCh. 12 - Prob. 17CQCh. 12 - Prob. 18CQCh. 12 - Prob. 19CQCh. 12 - Prob. 20CQCh. 12 - Prob. 21CQCh. 12 - Prob. 22CQCh. 12 - Prob. 23CQCh. 12 - Prob. 24CQCh. 12 - Prob. 25CQCh. 12 - Prob. 26CQCh. 12 - Prob. 27CQCh. 12 - Prob. 28CQCh. 12 - Prob. 1ETSQCh. 12 - Prob. 2ETSQCh. 12 - Prob. 3ETSQCh. 12 - Prob. 4ETSQCh. 12 - Prob. 5ETSQCh. 12 - Prob. 6ETSQCh. 12 - Prob. 7ETSQCh. 12 - Prob. 8ETSQCh. 12 - Prob. 9ETSQCh. 12 - Prob. 10ETSQCh. 12 - In Example Problem 12.1, a uniaxial composite...Ch. 12 - Prob. 12.2PCh. 12 - Prob. 12.3PCh. 12 - Prob. 12.4PCh. 12 - Prob. 12.5PCh. 12 - Prob. 12.6PCh. 12 - Estimate the transverse tensile strength of the...Ch. 12 - Prob. 12.8PCh. 12 - Prob. 12.9PCh. 12 - Prob. 12.10PCh. 12 - Prob. 12.11PCh. 12 - Prob. 12.12PCh. 12 - Prob. 12.13PCh. 12 - Prob. 12.14PCh. 12 - Prob. 12.15PCh. 12 - Prob. 12.16PCh. 12 - Prob. 12.17P
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- The stress-strain diagram of reinforcement steel having a cross-sectional diameter of 12 mm diameter and 100 mm gage length is determined after its tensile strength test as follows. Based on the stress-strain diagram determine the followings properties of the material (Poisson’s ratio of the material is 0.32) a) Resilienceb) Shear modulusc) Bulk modulusd) Ductility as described by the percent change in lengtharrow_forwardtie bars (in mm, round off to the nearest Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and concrete is 2 MPa, and the joint gap between the slabs is 10 mm. Ignoring the loss of bond and the tolerance factor, the design length of the integer) isarrow_forward(d) What is the role of surface energies of both matrix and reinforcements in order to enhance the fracture toughness of the composite?arrow_forward
- A steel bar and an aluminum bar are bonded together as shown to form a composite beam. Knowing that the vertical shear in the beam is 4 kips and that the modulus of elasticity is 29 * 106 psi for the steel and 10.6 *106 psi for the aluminum, determine (a) the aver-age shearing stress at the bonded surface, (b) the maximum shearing stress in the beam.arrow_forwardTie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer) isarrow_forwardDetermine the x-bar centroid of the composite figure shown. Where: x=5 ftShow your solution and round off if possiblearrow_forward
- The flexural strength (fr) of concrete measured from the bending test is always higher than the direct tensile strength (ft). In reality, the stress in the cracked part of the concrete is lower than ft. Also, failure may occur on the compressive side. Assuming NO tension softening (i.e., the stress in the cracked part stays at ft) and infinite compressive strength (i.e., compressive failure will never occur), draw the stress distribution over the depth of the beam at ultimate failure when the curvature of the section is approaching infinity. With this stress distribution, show that the upper bound of fr/ft is equal to 3. (Hint: On rotating the section, because the compressive stress can increase well beyond ft, the neutral axis will continue to shift upwards.)arrow_forwardDetermine the x-bar centroid of the composite figure shown. Where r=42 mmShow your solutionarrow_forwardIt is necessary to fabricate an aligned and discontinuous carbon fibre-epoxy matrix composite having a longitudinal tensile strength of 1900 MPa using 0.45 volume fraction of fibres. Compute the required fibre fracture strength assuming that the average fibre diameter and length are 8 × 10-3 mm and 3.5 mm, respectively. The fibre-matrix bond strength is 40 MPa, and the matrix stress at fibre failure is 12 MPa. Note that reasonable fibre fracture strength should normally be in the range of ~1.4 GPa – 20 GPa. (Hint: use equations 16.3 for critical fibre length and 16.18 for discontinuous and aligned fibre composites).arrow_forward
- Determine the maximum moment of inertia of the composite figure shown below, in mm^4.arrow_forwardA composite beam is made of two brass [E - 111 GPa] bars bonded to two aluminum [E - 72 GPa] bars, as shown. The beam is subjected to a bending moment of 250 N-macting about the z axis. Using a - 10 mm, b- 65 mm, c- 20 mm, and d- 45 mm, calculate (a) the maximum bending stress in the aluminum bars. (b) the maximum bending stress in the brass bars. Aluminum Brass Brass Aluminum Answers: (a) Oa i MPa (b) Oer MPa Save for Later Attempts: 0 of 1 used Submit Answerarrow_forwardThe load-strain data obtained in a tension test of a unidirectional carbon fiber/epoxy composite are given below. The specimen dimensions are length=254 mm, width=12.7 mm and thickness is 1.4 mm. Determine the tensile modulus and Poisson ration for each fiber orientation Axial strain Load (N) Transverse strain % 自 % 0° 45° 90° 0° 45° 90° 0.05 2130 130 67 -0.012 -0.113 -0.0004 0.10 4270 255 134 -0.027 -0.021 -0.001 0.15 6400 360 204 -0.041 -0.029 -0.0014 0.20 8620 485 333 -0.054 -0.038 -0.0019 0.25 565 396 -0.048 -0.0025arrow_forward
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