751.32 Concrete Pile Cap Intermediate Bents

751.32.1 General

751.32.1.1 Material Properties

Concrete
Typically, shall consist of:
	Class B Concrete (Substructure)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f'_c}	= 3.0 ksi
		Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, n}	= 10

In addition, Class B-1 Concrete (Substructure) may also be used in special cases (See Project Manager). The following equations shall apply to both concrete classes:

Concrete modulus of elasticity:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, E_c = 33000 K_l w_c \sqrt [1.5]{f'_c}}

Where:

$\,w_{c}$	= unit weight of non-reinforced concrete = 0.145 kcf
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, K_l}	= correction factor for source of aggregate = 1.0

Modulus of Rupture:	For minimum reinforcement,	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_r = 0.37 \sqrt {f'_c}}
	For all other calculations,	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_r = 0.24 \sqrt {f'_c}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \sqrt{f'_c}}  is in units of ksi

Reinforcing Steel

Minimum yield strength,	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f_y}	= 60.0 ksi
Steel modulus of elasticity,	$\,E_{s}$	= 29000 ksi

751.32.2 Design

751.32.2.1 Limit States and Factors

In general, each component shall satisfy the following equation:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Q = \sum \eta_i \gamma_i Q_i \le \phi R_n = R_r}

Where:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Q}	= Total factored force effect
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Q_i}	= Force effect
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \eta}	= Load modifier
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \gamma_i}	= Load factor
$\,\phi$	= Resistance factor
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, R_n}	= Nominal resistance
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, R_r}	= Factored resistance

Limit States

The following limit states shall be considered for bent design:

STRENGTH – I

STRENGTH – III

STRENGTH – IV

STRENGTH – V

SERVICE – I

FATIGUE

See LRFD Table 3.4.1-1 and LRFD 3.4.2 for Loads and Load Factors applied at each given limit state.

Resistance factors

STRENGTH limit states, see LRFD 5.5.4.2

For all other limit states, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi} = 1.00

Load Modifiers

751.32.3 Details

751.32.3.1 General

(*) 3" (Typ.)
Part Elevation	Part Section

	Use 2'-6" minimum or as determined by the superstructure requirements or the minimum support length required for earthquake criteria (expansion joint bents only) (3" increments).
	= 2'-9" (Min.) for Wide Flange and Double-Tee Girders or,    3'-0" (Min.) for Prestressed Girders and Plate Girders.
	Check the clearance of the anchor bolt well to the top of pile. Increase the beam depth if needed.
	If the depth at the end of the beam, due to the steps, exceeds 4~6", the beam bottom should be stepped or sloped.
	Use 3/4" bevel strip if expansion device is located at bent. Continue to use 1-1/2" clear to reinforcing steel in bottom of beam.
	Minimum of 3 piles at 10'-0" cts., maximum spacing (1" increments).

751.32.3.2 Front Sheet

Note:	The following are details and dimensions for the Plan View on the Front Sheets.
	Details for unsymmetrical roadways will require dimensions tying Centerline Lane to Centerline Structure.

751.32.4 Reinforcement

751.32.4.1 General

Part Elevation	Section Thru Beam
Part Plan

Note:	Locate #4 bars "" under bearings where required to maintain a 6" maximum spacing of combined stirrups. (#4 bars "" are not required for Double-Tee Structures.)
	When an expansion device is used at an intermediate bent, all reinforcement located entirely within the beam or extending into the beam shall be epoxy coated.

	* #4 Bars () not required for Double-Tee structures
Reinforcement Under Bearings
Transverse Beam Steps - Over 3" or Steps Accumulating Over 3"

Part Plan
Over 3" thru 12"	Over 12"
Longitudinal Beam Steps