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Part II. (60 points) Calculation and Discussion Questions

Problem No.1

The gel/space ratio in cement paste is given by:



(a)
(3%) A cement specimen is cured in water for a long time. Microscopic examination confirms that all the cement has reacted. The porosity inside the hardened cement is found to be 20%. What is the w/c ratio of the mix?


(b)
(2%) What is the critical w/c ratio below which there is insufficient space for all the cement grains to hydrate?


(c)
(3%) For another cement specimen, after curing for a long time, microscopic examination indicates that the porosity is very close to zero. It is found that only 75% of the cement has reacted. What is the w/c ratio of the mix?


(d)
(2%) When there is air entrainment, how should the above equation for X be modified? Give a precise definition of any term you add to the equation.





Problem No.2

(a)
(5%) After going through the mix design process, the following mix proportion is determined for one cubic meter of concrete.

Water : 180 kg
Cement: 320 kg
Sand (SSD): 600 kg
Coarse Aggregate (SSD): 1,300 kg
The sand and aggregates in the batching plant are found to be under the following moisture condition:
Sand: MC (SSD) = 1.5%
Coarse Aggregate: MC (OD) = 2%, Absorption = 3%
How should the above mix proportion be modified to maintain the design properties?

(b)
(2%) To ensure concrete durability, both the w/c ratio and cement content need to be kept above a minimum. Why?





(c)
(2%) In placing concrete, why is it desirable to place concrete as near as possible to its final position? After concrete is placed, what is the purpose of compaction?


(d)
(3%) After placing and compaction, if the surface of a concrete slab is NOT kept wet, what are the two major problems that will arise? Briefly explain.




Problem No.3 (12%)
? ?
(a) (b)

z
100 100
y 100
100
x

(Note: Balancing stresses exist on opposite faces of the block)

(a)
(4%) A piece of steel is under a tensile stress of 100 MPa along the x-axis and a compression of 100 MPa along the y-axis. The uniaxial yield strength of the steel is 300 MPa. What is the applied tension along the z-axis to cause yielding, using


(i)
the Tresca criterion


(ii)
the von Mises criterion




Draw, with respect to the x-y-z axes, the plane on which shear failure will occur according to the Tresca criterion
(b) (4%) If the above piece of steel is under a pure shear of 100 MPa in the x-y plane instead, find the applied tension in the z-direction to cause yielding, using
(i) the Tresca criterion
(ii) the von Mises criterion
Draw, with respect to the x-y-z axes, the plane on which shear failure will occur according to the Tresca criterion
(c) (4%) When metal