Homework 7 Solution

# Homework 7 Solution - MEEN 222-502 Fall 2008 Homework#7 Due...

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MEEN 222-502 Fall 2008 Homework #7 Due: 26 November 2008 at the beginning of class 1. Callister 16.4 (a) Concrete consists of an aggregate of particles that are bonded together by cement. (b) Three limitations of concrete are: (1) it is a relatively weak and brittle material; (2) it experiences relatively large thermal expansions (contractions) with changes in temperature; and (3) it may crack when exposed to freeze-thaw cycles. (c) Three reinforcement strengthening techniques are: (1) reinforcement with steel wires, rods, etc.; (2) reinforcement with fine fibers of a high modulus material; and (3) introduction of residual compressive stresses by prestressing or posttensioning. 2. Callister 16.13 The problem stipulates that the cross-sectional area of a composite, Ac , is 480 mm 2 (0.75 in. 2 ), and the longitudinal load, F c , is 53,400 N (12,000 lbf) for the composite described in Problem 16.8. (a) First, we are asked to calculate the F f /F m ratio. According to Equation 16.11 ( )( ) ( )( ) 7 . 44 0.55 GPa 2.4 0.45 GPa 131 = = = m m f f m f V E V E F F or F f =44.7 F m (b) Now, the actual loads carried by both phases are called for. From Equation 16.4 N 400 , 53 7 . 44 N 400 , 53 = + = = + m m c m f F F F F F which leads to N 232 , 52 N 1168 N 400 , 53 N 1168 = = = = m c f m F F F F (c) To compute the stress on each of the phases, it is first necessary to know the cross- sectional areas of both fiber and matrix. These are determined as

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