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(CIVL111)final021.pdf
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FINAL EXAMINATION for CIVL 111 (Spring 2000) II.(50 points) Calculations
Problem No.1 (10%)
The material ratio for concrete mix is 1:1.5:2 (C:Sand:Coarse Aggregate by weight). The BSG for cement is 3.15, for sand is 2.5 and for coarse aggregate is 2.7. Air content is 4.8%. The gel/space ratio is 0.72. Calculate the water cement ratio (=0.8) ?
Problem No.2 (10%)
A continuous fiber reinforced cement (FRC) specimen is loaded in uniaxial tension. The Young's modulus of cement paste is 20 GPa and tension strength is 5 MPa. The Young's modulus of fiber is 210 GPa.
If Vf is 3% and total 25 fibers with a diameter of 0.2 mm used, when the stress in FRC reaches 6 MPa, what is stress in fiber ? Will the cement paste crack ? What is the load carried by the specimen ?
Problem No.3
(a) (3%) A cube is made of metal with 200 MPa yield strength. The three faces of the cube are perpendicular to the x, y and z axes. A compressive stress of 100 MPa is applied along the z-direction. Find the tensile stress along the x-direction to cause material yielding, using
(i) the Tresca criterion (draw the critical Mohr circle)
(ii) the von Mises criterion
(b) (3%) If a compressive stress is applied along the x-direction instead, find the magnitude of the stress to cause material yielding, using
(i)
the Tresca criterion (draw the critical Mohr circle)
(ii)
the von Mises criterion
(c)
(3%) If the two faces perpendicular to the y-axis are fixed (i.e., no strain along the y-direction is allowed, re-do part (b), using the Tresca criterion ONLY. Take the Poissons ratio of the material to be 0.2.
Problem No.4
(a) (4%) A metallic plate of 1 meter width contains a through crack of size 2a = 1 mm at the middle. A tensile stress is applied perpendicular to the crack. Fracture occurs when the applied stress is 50 MPa.
(i) What is the fracture toughness of the metal
(ii) If the yield strength of the metal is 100 MPa, find the maximum allowable crack size in the plate if brittle fracture is to be avoided.
(b) (4%) A metallic plate containing a small crack is subject to cyclic loading of uniform amplitude (). Assume crack propagation to follow the Paris law:
da/
dN = A()n, where n = 4
It is
found that the crack size is doubled after 10,000 cycles of loading. Under the same magnitude of cyclic loading, how many more cycles will it take for the crack size to become 4 times the initial size? (You can assume the critical crack size has not yet been reached.)
(c
) (2%) The Paris Law for fatigue crack growth is based on Linear Elastic Fracture Mechanics. Does it apply to high cycle or low cycle fatigue? Briefly explain in a few sentences.
Problem No.5
The time dependent behaviour of a given material is represented by the above parallel model.
For the dashpot:
d/dt = /, where is t