Anchorage set losses - Revision history

Ok: Text replacement - "" to ""

2024-10-22T00:24:25Z

Text replacement - "</tex>" to "</math>"

← Older revision		Revision as of 02:24, 22 October 2024
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	Anchorage set losses are caused by the movement of the tendon prior to seating of the [[wedge\|wedges]] or the [[anchorage\|anchorage gripping device]]. A common value of these losses is about 10mm (AASHTO LRFD 2007).		Anchorage set losses are caused by the movement of the tendon prior to seating of the [[wedge\|wedges]] or the [[anchorage\|anchorage gripping device]]. A common value of these losses is about 10mm (AASHTO LRFD 2007).

	If <math>\Delta_a</~~tex~~> is the anchorage slip and <math>L_a</~~tex~~> is the length along the tendon affected by the anchorage slip (Choudry 1986), then:		If <math>\Delta_a</math> is the anchorage slip and <math>L_a</math> is the length along the tendon affected by the anchorage slip (Choudry 1986), then:

	<math>\Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx</~~tex~~>		<math>\Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx</math>

	where <math>\Delta_{\epsilon}</~~tex~~> is the decrease in the tendon strain due to anchorage slip.		where <math>\Delta_{\epsilon}</math> is the decrease in the tendon strain due to anchorage slip.

	=== Uniform distribution of anchorage losses ===		=== Uniform distribution of anchorage losses ===

	Assuming that the anchorage slip losses are uniformly distributed over the entire length of the tendon (in other words <math>\Delta_{\epsilon}</~~tex~~> is constant), then the following equations can be written:		Assuming that the anchorage slip losses are uniformly distributed over the entire length of the tendon (in other words <math>\Delta_{\epsilon}</math> is constant), then the following equations can be written:

	<math>\Delta_a = \Delta_{\epsilon} L</~~tex~~>		<math>\Delta_a = \Delta_{\epsilon} L</math>

	<math>\Delta_{\epsilon} = \frac{\Delta_a}{L}</~~tex~~>		<math>\Delta_{\epsilon} = \frac{\Delta_a}{L}</math>

	Noting that		Noting that

	<math>\Delta_{\sigma} = E_p \Delta_{\epsilon}</~~tex~~> and <math>\Delta F = A_p \Delta \sigma</~~tex~~>		<math>\Delta_{\sigma} = E_p \Delta_{\epsilon}</math> and <math>\Delta F = A_p \Delta \sigma</math>

	we can write the final equation for the loss of prestress force:		we can write the final equation for the loss of prestress force:

	<math>\Delta F = A_p E_p \frac{\Delta_a}{L}</~~tex~~>		<math>\Delta F = A_p E_p \frac{\Delta_a}{L}</math>

	where:		where:

	* <math>A_p</~~tex~~> ... area of the prestressing tendon		* <math>A_p</math> ... area of the prestressing tendon
	* <math>E_p</~~tex~~> ... [[Young's modulus]] of the prestressing tendon		* <math>E_p</math> ... [[Young's modulus]] of the prestressing tendon
	* <math>\Delta F</~~tex~~> ... loss of prestressing force		* <math>\Delta F</math> ... loss of prestressing force
	* <math>L</~~tex~~> ... length of the tendon		* <math>L</math> ... length of the tendon

	== References ==		== References ==

Ok: Text replacement - "" to " $"$

2024-10-22T00:15:56Z

Text replacement - "<tex>" to "<math>"

Ok at 17:54, 24 August 2010

2010-08-24T17:54:32Z

← Older revision		Revision as of 19:54, 24 August 2010
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	<tex>\Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx</tex>		<tex>\Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx</tex>

	where <tex>\Delta_{\epsilon}</tex> is the decrease in the tendon due to anchorage slip.		where <tex>\Delta_{\epsilon}</tex> is the decrease in the tendon strain due to anchorage slip.

	=== Uniform distribution of anchorage losses ===		=== Uniform distribution of anchorage losses ===

Ok at 17:53, 24 August 2010

2010-08-24T17:53:42Z

← Older revision		Revision as of 19:53, 24 August 2010
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	Anchorage set losses are caused by by the movement of the tendon prior to seating of the [[wedge\|wedges]] or the [[anchorage\|anchorage gripping device]]. A common value of these losses is about 10mm (AASHTO LRFD 2007).		Anchorage set losses are caused by the movement of the tendon prior to seating of the [[wedge\|wedges]] or the [[anchorage\|anchorage gripping device]]. A common value of these losses is about 10mm (AASHTO LRFD 2007).

	If <tex>\Delta_a</tex> is the anchorage slip and <tex>L_a</tex> is the length along the tendon affected by the anchorage slip (Choudry 1986), then:		If <tex>\Delta_a</tex> is the anchorage slip and <tex>L_a</tex> is the length along the tendon affected by the anchorage slip (Choudry 1986), then:

Ok at 21:31, 22 April 2009

2009-04-22T21:31:18Z

← Older revision		Revision as of 23:31, 22 April 2009
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	Anchorage set losses are caused by by the movement of the tendon prior to seating of the [[wedge\|wedges]] or the [[anchorage\|anchorage gripping device]]. A common value of these losses is about 10mm (AASHTO LRFD 2007).		Anchorage set losses are caused by by the movement of the tendon prior to seating of the [[wedge\|wedges]] or the [[anchorage\|anchorage gripping device]]. A common value of these losses is about 10mm (AASHTO LRFD 2007).

	If <tex>\Delta_a</tex> is the anchorage slip and <tex>L_a</tex> is the length along the tendon affected by the anchorage slip, then:		If <tex>\Delta_a</tex> is the anchorage slip and <tex>L_a</tex> is the length along the tendon affected by the anchorage slip (Choudry 1986), then:

	<tex>\Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx</tex>		<tex>\Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx</tex>

Ok at 21:28, 22 April 2009

2009-04-22T21:28:47Z

← Older revision		Revision as of 23:28, 22 April 2009
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	== References ==		== References ==

	* AASHTO LRFD Bridge Design Specifications, SI Units, 4th Edition, 2007; Article 5.9.5.2.1, p. 5-109		* AASHTO LRFD Bridge Design Specifications, SI Units, 4th Edition, 2007; Article 5.9.5.2.1, p. 5-109
			* Deepak Choudry: Analysis of Curved Nonprismatic Reinforced and Prestressed Concrete Box Girder Bridges, Report No. UCB/SEMM-86/13, December 1986; p. 45 (Section 3.4.2: Anchorage Slip Losses)

	{{Prestressed Concrete}}		{{Prestressed Concrete}}

Ok at 21:25, 22 April 2009

2009-04-22T21:25:45Z

← Older revision		Revision as of 23:25, 22 April 2009
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			Anchorage set losses are caused by by the movement of the tendon prior to seating of the [[wedge\|wedges]] or the [[anchorage\|anchorage gripping device]]. A common value of these losses is about 10mm (AASHTO LRFD 2007).

	If <tex>\Delta_a</tex> is the anchorage slip and <tex>L_a</tex> is the length along the tendon affected by the anchorage slip, then:		If <tex>\Delta_a</tex> is the anchorage slip and <tex>L_a</tex> is the length along the tendon affected by the anchorage slip, then:

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	* <tex>\Delta F</tex> ... loss of prestressing force		* <tex>\Delta F</tex> ... loss of prestressing force
	* <tex>L</tex> ... length of the tendon		* <tex>L</tex> ... length of the tendon

			== References ==

			* AASHTO LRFD Bridge Design Specifications, SI Units, 4th Edition, 2007; Article 5.9.5.2.1, p. 5-109

	{{Prestressed Concrete}}		{{Prestressed Concrete}}

Ok: /* Uniform distribution of anchorage losses */

2009-04-22T21:19:55Z

Uniform distribution of anchorage losses

← Older revision		Revision as of 23:19, 22 April 2009
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	<tex>\Delta_a = \Delta_{\epsilon} L</tex>		<tex>\Delta_a = \Delta_{\epsilon} L</tex>

	<tex>\Delta_{\epsilon} = \Delta_a / L</tex>		<tex>\Delta_{\epsilon} = \frac{\Delta_a}{L}</tex>

	Noting that		Noting that

Ok at 21:18, 22 April 2009

2009-04-22T21:18:16Z

← Older revision		Revision as of 23:18, 22 April 2009
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	where <tex>\Delta_{\epsilon}</tex> is the decrease in the tendon due to anchorage slip.		where <tex>\Delta_{\epsilon}</tex> is the decrease in the tendon due to anchorage slip.

			=== Uniform distribution of anchorage losses ===

	Assuming that the anchorage slip losses are uniformly distributed over the entire length of the tendon (in other words <tex>\Delta_{\epsilon}</tex> is constant), then the following equations can be written:		Assuming that the anchorage slip losses are uniformly distributed over the entire length of the tendon (in other words <tex>\Delta_{\epsilon}</tex> is constant), then the following equations can be written:
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	* <tex>A_p</tex> ... area of the prestressing tendon		* <tex>A_p</tex> ... area of the prestressing tendon
	* <tex>E_p</tex> ... [[Young's modulus]] of the prestressing tendon		* <tex>E_p</tex> ... [[Young's modulus]] of the prestressing tendon
	* <tex>\Delta F<\tex> ... loss of prestressing force		* <tex>\Delta F</tex> ... loss of prestressing force
	* <tex>L</tex> ... length of the tendon		* <tex>L</tex> ... length of the tendon
	{{Prestressed Concrete}}		{{Prestressed Concrete}}

Ok: New page: If \Delta_a is the anchorage slip and L_a is the length along the tendon affected by the anchorage slip, then: \Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx
2009-04-22T21:16:31Z

New page: If <tex>\Delta_a</tex> is the anchorage slip and <tex>L_a</tex> is the length along the tendon affected by the anchorage slip, then: <tex>\Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx</tex...

New page
If <tex>\Delta_a</tex> is the anchorage slip and <tex>L_a</tex> is the length along the tendon affected by the anchorage slip, then:

<tex>\Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx</tex>

where <tex>\Delta_{\epsilon}</tex> is the decrease in the tendon due to anchorage slip.

Assuming that the anchorage slip losses are uniformly distributed over the entire length of the tendon (in other words <tex>\Delta_{\epsilon}</tex> is constant), then the following equations can be written:

<tex>\Delta_a = \Delta_{\epsilon} L</tex>

<tex>\Delta_{\epsilon} = \Delta_a / L</tex>

Noting that

<tex>\Delta_{\sigma} = E_p \Delta_{\epsilon}</tex> and <tex>\Delta F = A_p \Delta \sigma</tex>

we can write the final equation for the loss of prestress force:

<tex>\Delta F = A_p E_p \frac{\Delta_a}{L}</tex>

where:

* <tex>A_p</tex> ... area of the prestressing tendon
* <tex>E_p</tex> ... [[Young's modulus]] of the prestressing tendon
* <tex>\Delta F<\tex> ... loss of prestressing force
* <tex>L</tex> ... length of the tendon
{{Prestressed Concrete}}

← Older revision		Revision as of 02:15, 22 October 2024
Line 1:		Line 1:
	Anchorage set losses are caused by the movement of the tendon prior to seating of the [[wedge\|wedges]] or the [[anchorage\|anchorage gripping device]]. A common value of these losses is about 10mm (AASHTO LRFD 2007).		Anchorage set losses are caused by the movement of the tendon prior to seating of the [[wedge\|wedges]] or the [[anchorage\|anchorage gripping device]]. A common value of these losses is about 10mm (AASHTO LRFD 2007).

	If <~~tex~~>\Delta_a</tex> is the anchorage slip and <~~tex~~>L_a</tex> is the length along the tendon affected by the anchorage slip (Choudry 1986), then:		If <math>\Delta_a</tex> is the anchorage slip and <math>L_a</tex> is the length along the tendon affected by the anchorage slip (Choudry 1986), then:

	<~~tex~~>\Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx</tex>		<math>\Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx</tex>

	where <~~tex~~>\Delta_{\epsilon}</tex> is the decrease in the tendon strain due to anchorage slip.		where <math>\Delta_{\epsilon}</tex> is the decrease in the tendon strain due to anchorage slip.

	=== Uniform distribution of anchorage losses ===		=== Uniform distribution of anchorage losses ===

	Assuming that the anchorage slip losses are uniformly distributed over the entire length of the tendon (in other words <~~tex~~>\Delta_{\epsilon}</tex> is constant), then the following equations can be written:		Assuming that the anchorage slip losses are uniformly distributed over the entire length of the tendon (in other words <math>\Delta_{\epsilon}</tex> is constant), then the following equations can be written:

	<~~tex~~>\Delta_a = \Delta_{\epsilon} L</tex>		<math>\Delta_a = \Delta_{\epsilon} L</tex>

	<~~tex~~>\Delta_{\epsilon} = \frac{\Delta_a}{L}</tex>		<math>\Delta_{\epsilon} = \frac{\Delta_a}{L}</tex>

	Noting that		Noting that

	<~~tex~~>\Delta_{\sigma} = E_p \Delta_{\epsilon}</tex> and <~~tex~~>\Delta F = A_p \Delta \sigma</tex>		<math>\Delta_{\sigma} = E_p \Delta_{\epsilon}</tex> and <math>\Delta F = A_p \Delta \sigma</tex>

	we can write the final equation for the loss of prestress force:		we can write the final equation for the loss of prestress force:

	<~~tex~~>\Delta F = A_p E_p \frac{\Delta_a}{L}</tex>		<math>\Delta F = A_p E_p \frac{\Delta_a}{L}</tex>

	where:		where:

	* <~~tex~~>A_p</tex> ... area of the prestressing tendon		* <math>A_p</tex> ... area of the prestressing tendon
	* <~~tex~~>E_p</tex> ... [[Young's modulus]] of the prestressing tendon		* <math>E_p</tex> ... [[Young's modulus]] of the prestressing tendon
	* <~~tex~~>\Delta F</tex> ... loss of prestressing force		* <math>\Delta F</tex> ... loss of prestressing force
	* <~~tex~~>L</tex> ... length of the tendon		* <math>L</tex> ... length of the tendon

	== References ==		== References ==