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Prestressed concrete beams are sometimes manufactured in the following manner. High-strength steel wires are stretched by a jacking mechanism that applies a force Q, as represented schematically in part a of the figure. Concrete is then poured around the wires to form a beam, as shown in the figure part b. After the concrete sets properly, the jacks are released, and the force Q is removed (see part c of the figure). Thus, the beam is left in a prestressed condition with the wires in tension and the concrete in compression. Assume that the prestressing force Q produces in the steel wires an initial stress a 0 = 620 MPa. If the module of elasticity of the steel and concrete are in the ratio 12:1 and the cross-sectional areas are in the ratio 1:50. what are the final stresses a 5 and a 5 in the two materials?

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Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

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Section
BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 2, Problem 2.5.30P
Textbook Problem
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Prestressed concrete beams are sometimes manufactured in the following manner. High-strength steel wires are stretched by a jacking mechanism that applies a force Q, as represented schematically in part a of the figure. Concrete is then poured around the wires to form a beam, as shown in the figure part b.

After the concrete sets properly, the jacks are released, and the force Q is removed (see part c of the figure). Thus, the beam is left in a prestressed condition with the wires in tension and the concrete in compression.

Assume that the prestressing force Q produces in the steel wires an initial stress a0= 620 MPa. If the module of elasticity of the steel and concrete are in the ratio 12:1 and the cross-sectional areas are in the ratio 1:50. what are the final stresses a5and a5 in the two materials?

  Chapter 2, Problem 2.5.30P, Prestressed concrete beams are sometimes manufactured in the following manner. High-strength steel

To determine

The final stresses sS and sCin the two materials.

Explanation of Solution

Given that,

Initial stress in the wires, s? = QAS= 620 MPa

AC = 50AS ES = 12EC

  

PS = Final compressive force in steel wires

PC = Final compressive force in concrete

From equilibrium equation,

  PS= PC (Eq. 1)

Initial elongation of steel wires:

d1 = QLESAS= σoLES

Final elongation of steel wires:

d2 = PSLESAS

Shortening of concrete:

d3 = PcLEcAc

  Now,δ1 δ2= δ3

? σoLESPSLESAS= PcLEcAc←(Eq

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Chapter 2 Solutions

Mechanics of Materials (MindTap Course List)
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