751.40 LFD Widening and Repair (CONTINUED) - Revision history

Hoskir: /* 751.40.8.15.4.3 Counterfort Walls */ updated old math symbols

2026-01-15T21:33:30Z

751.40.8.15.4.3 Counterfort Walls: updated old math symbols

← Older revision		Revision as of 16:33, 15 January 2026
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	[[image:751.24.3.2.3 counterfort.jpg\|center\|800px]]		[[image:751.24.3.2.3 counterfort.jpg\|center\|800px]]

	:<math>P = C_a ~~\boldsymbol~~ \gamma_s</math>		:<math>P = C_a \gamma_s</math>

	:where:		:where:
	::''C<sub>a</sub>'' = coefficient of active earth pressure		::''C<sub>a</sub>'' = coefficient of active earth pressure

	::<math>~~\boldsymbol~~ \gamma_s</math> = unit weigt of soil		::<math>\gamma_s</math> = unit weigt of soil

	Design the wall to support horizontal load from the earth pressure and the liveload surcharge (if applicable) as outlined on the previous pages and as designated in AASHTD Section 3.20, except that maximum horizontal loads shall be the calculated equivalent fluid pressure at 3/4 height of wall [(0.75 H)P] which shall be considered applied uniformly from the lower quarter point to the bottom of wall.		Design the wall to support horizontal load from the earth pressure and the liveload surcharge (if applicable) as outlined on the previous pages and as designated in AASHTD Section 3.20, except that maximum horizontal loads shall be the calculated equivalent fluid pressure at 3/4 height of wall [(0.75 H)P] which shall be considered applied uniformly from the lower quarter point to the bottom of wall.

Hoskir: /* 751.40.8.15.4.2 Pile Footings */ updated old math equations

2026-01-15T21:32:35Z

751.40.8.15.4.2 Pile Footings: updated old math equations

← Older revision		Revision as of 16:32, 15 January 2026
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	:::<math>F = \frac{1}{2}\gamma_s C_P H^2 B </math> , where: <math> C_P = tan^2\Big[45 + \frac{\phi}{2}\Big]</math>		:::<math>F = \frac{1}{2}\gamma_s C_P H^2 B </math> , where: <math> C_P = tan^2\Big[45 + \frac{\phi}{2}\Big]</math>

	:::<math>~~\boldsymbol~~{\gamma_s}</math> = unit weight of soil		:::<math>{\gamma_s}</math> = unit weight of soil

	:::''H'' = depth of pile considered for lateral resistance (H<sub>max</sub>= 6B)		:::''H'' = depth of pile considered for lateral resistance (H<sub>max</sub>= 6B)
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	:::''B'' = width of pile		:::''B'' = width of pile

	:::<math>~~\boldsymbol~~{\phi}</math> = angle of internal friction of soil		:::<math>{\phi}</math> = angle of internal friction of soil

	[[image:751.24.3.2.2 resistance passive.jpg\|center\|450px]]		[[image:751.24.3.2.2 resistance passive.jpg\|center\|450px]]

Hoskir: /* 751.40.8.15.4.1 Spread Footings */ updated old math equation

2026-01-15T21:31:20Z

751.40.8.15.4.1 Spread Footings: updated old math equation

Hoskir: /* 751.40.8.15 Cast-In-Place Concrete Retaining Walls */ updated old math code

2026-01-15T21:28:28Z

751.40.8.15 Cast-In-Place Concrete Retaining Walls: updated old math code

← Older revision		Revision as of 16:28, 15 January 2026
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	:''H'' = height of the soil face at the vertical plane of interest		:''H'' = height of the soil face at the vertical plane of interest

	:<math>~~\boldsymbol~~{\gamma_s}</math> = unit weight of soil		:<math>{\gamma_s}</math> = unit weight of soil

	:<math>~~\boldsymbol~~{\delta}</math>= slope of fill in degrees		:<math>{\delta}</math>= slope of fill in degrees

	:<math>~~\boldsymbol~~{\phi}</math> = angle of internal friction of soil in degrees		:<math>{\phi}</math> = angle of internal friction of soil in degrees
	[[image:751.24.1.2.jpg\|center\|485px]]		[[image:751.24.1.2.jpg\|center\|485px]]

Hoskir: split page due to formulas not working

2025-04-28T15:26:35Z

split page due to formulas not working

← Older revision		Revision as of 10:26, 28 April 2025
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	::Key length = divide length "A" or "B" into an odd number of spaces of equal lengths. Each space length shall not exceed 24 inches. Use as few spaces as possible with the minimum number of spaces equal to three (or one key).		::Key length = divide length "A" or "B" into an odd number of spaces of equal lengths. Each space length shall not exceed 24 inches. Use as few spaces as possible with the minimum number of spaces equal to three (or one key).


			[[Category:751 LRFD Bridge Design Guidelines]]

Hoskir: /* 751.40.8.11 Open Concrete Intermediate Bents and Piers */

2025-04-28T13:40:14Z

751.40.8.11 Open Concrete Intermediate Bents and Piers

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Hoskir at 13:17, 28 April 2025

2025-04-28T13:17:26Z

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Hoskir at 13:03, 28 April 2025

2025-04-28T13:03:14Z

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Hoskir: split page due to formulas not working

2025-04-28T12:53:37Z

split page due to formulas not working

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← Older revision		Revision as of 16:31, 15 January 2026
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	:''C<sub>p</sub>'' = coefficient of passive earth pressure		:''C<sub>p</sub>'' = coefficient of passive earth pressure

	:<math>~~\boldsymbol~~{\gamma_s}</math> = unit weight of soil		:<math>{\gamma_s}</math> = unit weight of soil

	:''H'' = height of the front face fill less than 1 ft. min. for erosion		:''H'' = height of the front face fill less than 1 ft. min. for erosion
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	:''y<sub>1</sub>'' = location of ''P<sub>p</sub>'' from bottom of footing		:''y<sub>1</sub>'' = location of ''P<sub>p</sub>'' from bottom of footing

	:<math>~~\boldsymbol~~{\phi}</math> = angle of internal friction of soil		:<math>{\phi}</math> = angle of internal friction of soil

	[[image:751.24.3.2.1 passive.jpg\|center\|500px]]		[[image:751.24.3.2.1 passive.jpg\|center\|500px]]
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	:<math>K_{PE} = \frac{\cos^2(\phi - \theta - \beta)}{\cos\theta\cos^2\beta\cos(\delta + \beta + \theta)\Bigg[1 + \sqrt{\frac{\sin(\phi + \delta)\sin(\phi - \theta - i)}{\cos(\delta + \beta + \theta)\cos(i - \beta)}}\Bigg]^2}</math>		:<math>K_{PE} = \frac{\cos^2(\phi - \theta - \beta)}{\cos\theta\cos^2\beta\cos(\delta + \beta + \theta)\Bigg[1 + \sqrt{\frac{\sin(\phi + \delta)\sin(\phi - \theta - i)}{\cos(\delta + \beta + \theta)\cos(i - \beta)}}\Bigg]^2}</math>

	::<math>~~\boldsymbol~~{\gamma}_s</math> = unit weight of soil		::<math>{\gamma}_s</math> = unit weight of soil

	:''H'' = height of soil at the location where the earth pressure is to be found		:''H'' = height of soil at the location where the earth pressure is to be found
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	:''k<sub>V</sub>'' = vertical acceleration coefficient		:''k<sub>V</sub>'' = vertical acceleration coefficient

	:<math>~~\boldsymbol~~{\phi}</math> = angle of internal friction of soil		:<math>{\phi}</math> = angle of internal friction of soil

	:<math>~~\boldsymbol~~{\theta} = arctan \big[\frac{k_h}{1 - k_V}\big]</math>		:<math>{\theta} = arctan \big[\frac{k_h}{1 - k_V}\big]</math>

	:''k<sub>H</sub>'' = horizontal acceleration coefficient		:''k<sub>H</sub>'' = horizontal acceleration coefficient

	:<math>~~\boldsymbol~~{\beta}</math> = slope of soil face in degrees		:<math>{\beta}</math> = slope of soil face in degrees

	:''i'' = backfill slope angle in degrees		:''i'' = backfill slope angle in degrees

	:<math>~~\boldsymbol~~{\delta}</math> = angle of friction between soil and wall		:<math>{\delta}</math> = angle of friction between soil and wall

	'''Special Soil Conditions'''		'''Special Soil Conditions'''

	Due to creep, some soft clay soils have no passive resistance under a continuing load. Removal of undesirable material and replacement with suitable material such as sand or crushed stone is necessary in such cases. Generally, this condition is indicated by a void ratio above 0.9, an angle of internal friction (<math>~~\boldsymbol~~{\phi}</math>) less than 22°, or a soil shear less than 0.8 ksf. Soil shear is determined from a standard penetration test.		Due to creep, some soft clay soils have no passive resistance under a continuing load. Removal of undesirable material and replacement with suitable material such as sand or crushed stone is necessary in such cases. Generally, this condition is indicated by a void ratio above 0.9, an angle of internal friction (<math>{\phi}</math>) less than 22°, or a soil shear less than 0.8 ksf. Soil shear is determined from a standard penetration test.

	:Soil Shear <math>\Big(\frac{k}{ft^2}\Big) = \frac{blows \ per\ 12\ in.}{10}</math>		:Soil Shear <math>\Big(\frac{k}{ft^2}\Big) = \frac{blows \ per\ 12\ in.}{10}</math>
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	is not readily available or is inconsistent, the friction factor (f) can be taken as		is not readily available or is inconsistent, the friction factor (f) can be taken as

	: ''f'' =<math>tan \Big(\frac{2\phi}{3}\Big)</math> where <math>~~\boldsymbol~~{\phi}</math> is the angle of internal friction of the soil (''Civil Engineering Reference Manual'' by Michael R. Lindeburg, 6th ed., 1992).		: ''f'' =<math>tan \Big(\frac{2\phi}{3}\Big)</math> where <math>{\phi}</math> is the angle of internal friction of the soil (''Civil Engineering Reference Manual'' by Michael R. Lindeburg, 6th ed., 1992).

	{\| border="1" class="wikitable" style="margin: 1em auto 1em auto"		{\| border="1" class="wikitable" style="margin: 1em auto 1em auto"
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	\|colspan="2"\|<sup>'''a'''</sup> It is not necessary to check rock or shale for sliding due to embedment.		\|colspan="2"\|<sup>'''a'''</sup> It is not necessary to check rock or shale for sliding due to embedment.
	\|-		\|-
	\|colspan="2"\|<sup>'''b'''</sup> Caution should be used with soils with <math>~~\boldsymbol~~{\phi}</math> < 22° or soil shear < 0.8 k/sq.ft. (soft clay soils). Removal and replacement of such soil with suitable material should be considered.		\|colspan="2"\|<sup>'''b'''</sup> Caution should be used with soils with <math>{\phi}</math> < 22° or soil shear < 0.8 k/sq.ft. (soft clay soils). Removal and replacement of such soil with suitable material should be considered.
	\|}		\|}