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Arabian Journal for Science and Engineering

, Volume 44, Issue 10, pp 8149–8170 | Cite as

Numerical and Analytical Behavior of Beams Prestressed with Unbonded Internal or External Steel Tendons: A State-of-the-Art Review

  • Maha AlqamEmail author
  • Fadi Alkhairi
Review --Civil Engineering
  • 61 Downloads

Abstract

This paper presents a detailed state-of-the-art chronological account of past studies dating back to the late 1980s consisting of an overview of the vast majority of prediction equations for the stress at ultimate in prestressed unbonded internal or external steel tendons of simply supported concrete beams. The paper also details past studies carried out to investigate the complete nonlinear behavior of such beams throughout loading. Past and relevant studies were carefully reviewed in detail and then synthesized in the most reduced, yet accurately depicted, format in an effort to capture the pertinent highlights. For each review, the most relevant factors considered by the authors were highlighted, including span-to-depth ratio, second-order effects, length of the plastic hinge, friction and/or slippage at deviators, and experimental verification. An evaluation was carried out to compare and contrast the various nonlinear analysis studies using a simple tabulated format. Gaps were identified, and recommendations for future research were further proposed by the authors.

Keywords

External prestressing Unbonded tendons Nonlinear analysis Second-order effects Ultimate strength 

List of Symbols

Aps

Area of prestressed unbonded reinforcement

As

Area of non-prestressed tensile reinforcement

b

Beam width of a rectangular section

c

Depth of neutral axis at ultimate nominal strength

d

Distance from extreme compressive fiber to the centroid of the non-prestressed reinforcement

dps

Depth from the extreme to compressed fiber to the centroid of the pretsressing steel

e

Eccentricity of the unbonded prestressed reinforcement at any point along the beam

em

Eccentricity of the prestressing steel at midspan

es

Eccentricity of the prestressing steel at the support

Eps

Modulus of elasticity of the prestressing steel

fc

Stress in the concrete top fiber of a simply supported beam

fpe

Effective prestress in unbonded tendons

fps

Stress in the unbonded prestressed reinforcement at nominal strength

fpu

Characteristic (ultimate) strength of the prestressed reinforcement

fpy

Yield stress of unbonded tendons

fs

Stress in the non-prestressed tensile reinforcement

fy

Yield stress in the non-prestressed reinforcement

f′c

Concrete compressive strength

FDM

Finite difference method

FEM

Finite element method

FRP

Fiber-reinforced polymers

GIA

Generalized iterative analysis

Icr

Cracked moment of inertia

It

Transformed moment of inertia

L

Length of the simply supported beam

La

Length of the region of constant moment [17]

Lo

Length of the equivalent plastic region [42]

Lp

Length of the equivalent plastic hinge [54, 64]

Lt

Length of the undeformed external tendon between end anchorages [64]

L1

Length of the undeformed inclined external tendon between end anchorage and deviator [64]

Mext

External moment at any point x along the span

Mint

Internal moment at x along the span calculated from force and moment equilibrium

Mn

Moment at ultimate nominal strength

Mpl

Plastic moment calculated excluding unbonded prestressing force at ultimate

P

Concentrated load at midspan

P/2

Concentrated load at the third point

Rs

Stress increment reduction factor responsible for second-order effects [58]

Sd

Spacing of the deviators [43, 64]

Se

Elastic stiffness matrix

Sg

Geometric stiffness matrix

St

Tangent stiffness matrix

TP

A ps x f ps

x

Distance measured from simply supported end up to deviator at the third point [64]

Z

Shear span or the distance between the point of maximum moment and the point of contra flexure

Δ

Midspan deflection

Δfps

Stress increase in the unbonded tendons beyond effective prestress

ΔM

Midspan deflection [54]

Δεp

Average elongation in the unbonded external tendon at ultimate [64]

Δεps

Average elongation in the unbonded tendon at a specific loading stage

εcu

Strain at the concrete top fiber of a simply supported beam at ultimate

εps

Strain in the prestressed reinforcement obtained from the stress–strain curve

β1

A fraction between 0.65 and 0.85 used by the ACI Code to compute the width of the Whitney stress block

Φcr

Beam curvature assuming an elastic cracked section

Φpy

Beam curvature assuming yielding of the prestressed reinforcement

Φu

Beam curvature assuming ultimate nominal strength

Φy

Beam curvature assuming yielding of the non-prestressed reinforcement

Ω

Strain reduction coefficient of unbonded to bonded tendons

Ωcr

Strain reduction coefficient assuming elastic cracked analysis

Ωu

Strain reduction coefficient assuming ultimate nominal strength

ζ

Shape function that varies between 0 and 1 derived from experimental tests [64]

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Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringThe University of JordanAmmanJordan
  2. 2.Magna MEP Electromechanical LLCDubaiUAE

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