A prismatic bar AB of length L, crosssectionalarea A, modulus of elasticity E, and weightW hangs vertically under its own weight (see figure).(a) Derive a formula for the downward displacementδC of point C, located at distance h fromthe lower end of the bar.(b) What is the elongation δB of the entire bar?(c) What is the ratio β of the elongation of theupper half of the bar to the elongation of thelower half of the bar?(d) If bar AB is a riser pipe hanging from a drillrig at sea, what is the total elongation of thepipe? Let L = 1500 m, A = 0.0157 m2, andE = 210 GPa. See Appendix I for weight densitiesof steel and sea water. (See Probs. 1.4-2 and1.7-13 for additional figures.)
A prismatic bar AB of length L, crosssectional
area A, modulus of elasticity E, and weight
W hangs vertically under its own weight (see figure).
(a) Derive a formula for the downward displacement
δC of point C, located at distance h from
the lower end of the bar.
(b) What is the elongation δB of the entire bar?
(c) What is the ratio β of the elongation of the
upper half of the bar to the elongation of the
lower half of the bar?
(d) If bar AB is a riser pipe hanging from a drill
rig at sea, what is the total elongation of the
pipe? Let L = 1500 m, A = 0.0157 m2, and
E = 210 GPa. See Appendix I for weight densities
of steel and sea water. (See Probs. 1.4-2 and
1.7-13 for additional figures.)
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