Shear design of precast prestressed concrete NEXT beam bridges: A critical assessment

Abstract

Northeast extreme tee (NEXT) precast prestressed concrete beams have recently emerged as a promising solution to accelerate bridge construction and enhance the sustainability of bridges. To date, several studies on the live load distribution factor (LLDF) for moment and shear in NEXT F beam bridges have been reported, which indicated that using the AASHTO LRFD LLDF for moment in NEXT F beam bridges could provide a sufficient safety margin; however, a 20% increase in the LRFD LLDF for shear was recommended for the safety of shear design. This paper intended to investigate the required transverse shear reinforcements in NEXT F beam bridges by using a factor of 1.2 for the LRFD LLDF for shear. A comprehensive study was carried out by considering various parameters, including concrete strength, beam section, bridge section, and span length. Results from this study showed that providing the minimum transverse shear reinforcement could offer a sufficient safety margin for the shear design of NEXT F beam bridges, even with an increase of 20% on the LRFD LLDF for shear. It is recommended that a factor of 1.2 be used for the LRFD LLDF for shear to ensure a safe design of NEXT F beam bridges, though the minimum transverse reinforcements will be likely to control the shear design.

Keywords

Accelerated bridge construction NEXT beam prestressed concrete shear design

1 Introduction

Bridges in the US and abroad are facing various structural deteriorations due to steel corrosion, which have led to a great number of structurally deficient bridges that need regular maintenance, structural repair, or strengthening. As well-known, bridge maintenance and repair are expensive, which include direct and indirect costs (such as environmental, social, and economic impacts) [1]. Precast concrete elements can offer better durability and less construction time compared to cast-in-place (CIP) concrete; for these reasons, using precast concrete elements is gaining popularity for accelerated bridge construction [e.g., 2, 3]. Northeast extreme tee (NEXT) precast prestressed concrete beams were developed for such purpose by the Precast/Prestressed Concrete Institute (PCI) [4, 5]. Figure 1 shows a typical NEXT F beam section. It can be seen the NEXT F beam section consists of two beam stems with a constant stem spacing of 1524 mm (5 ft) on centers and a 101.6 mm (4 in) thick top flange; the beam flange has a minimum width of 2426 mm (noted as “8 ft wide beam”) and a maximum beam width of 3645 mm (noted as “12 ft wide beam”); the available beam depths are: 914.4 mm (36 in), 812.8 mm (32 in), 711.2 mm (28 in), and 609.6 mm (24 in), denoted as NEXT 36F, NEXT 32F, NEXT 28F, and NEXT 24F, respectively [4]. Table 1 shows the section properties of NEXT F beams. Figure 2 shows the bridges built with four NEXT F beams and a 203 mm (8 in) thick CIP concrete deck [4]. For NEXT F beam bridges, there is no need for intermediate diaphragms and shear keys; also, there is no need for concrete deck formwork, all of which contribute to the time saved on bridge construction [4 –6]. An example of a bridge replacement project using precast prestressed concrete NEXT beams was reported in [6], where the total time savings were estimated to be about 7 weeks for the erection of NEXT beam superstructure when compared to the Northeast Bulb Tee beam superstructure [6].

Fig. 1

NEXT F beam cross section (Adapted from [4]; Note: 1 ft = 304.8 mm).

Fig. 2

NEXT F beam bridge sections examined herein (Adapted from [4]; Unit: mm; S = beam spacing).

Table 1

NEXT F beam section properties (Adapted from [4])

Beam section		Beam width (in.)	Beam depth (in.)	Base stem width (in.)	Area (in²)	I (in⁴)	Y_b (in.)
8 ft wide	NEXT 36	95.5	36	13	1287	160240	21.77
	NEXT 32	95.5	32	13.25	1182	115813	19.51
	NEXT 28	95.5	28	13.5	1075	79901	17.24
	NEXT 24	95.5	24	13.75	966	51823	14.95
12 ft wide	NEXT 36	143.5	36	13	1479	185525	23.36
	NEXT 32	143.5	32	13.25	1374	134258	20.98
	NEXT 28	143.5	28	13.5	1267	92661	18.57
	NEXT 24	143.5	24	13.75	1158	60045	16.12

(Note: I = moment of inertia; Y_b = distance from bottom of beam to center of gravity; 1 in = 25.4 mm).

Table 2

Concrete strength, bridge section, beam section, and span length for the NEXT F beam bridges examined herein

Concrete strength	Bridge section	Bridge span length (Unit: ft)
		NEXT 24F		NEXT 28F		NEXT 32F		NEXT 36F
$f_{c}^{'} = 6 ksi$	I	40	47	48	54	55	61	62	68
$f_{ci}^{'} = 4 ksi$	II	36	37	38	45	46	51	52	57
$f_{c}^{'} = 8 ksi$	I	50	58	59	67	68	76	77	82
$f_{ci}^{'} = 6 ksi$	II	40	47	48	55	56	65	66	71
$f_{c}^{'} = 10 ksi$	I	55	66	67	73	74	80	81	86
$f_{ci}^{'} = 8 ksi$	II	50	58	59	63	65	70	71	75

(Note: 1 ft = 304.8 mm; 1 ksi = 6.895 MPa).

2 Research significance

Due to the unequal beam stem spacing in NEXT F beam bridges, the live load distribution factors (LLDF) from the AASHTO LRFD approximation equations may not be applicable for NEXT F beam bridges [4]. In recent years, several research projects on the LLDF for shear and moment in NEXT F beam bridges have shown that using the AASHTO LRFD LLDF for moment in NEXT F beam bridges could provide a sufficient safety margin; however, a 20% increase in the LRFD LLDF for shear is needed for shear safety [7, 8]. This increased live load shear in NEXT F beam bridges has posed a concern for the structural safety if the NEXT F beam bridge is designed with the LRFD LLDF for shear. Therefore, to fully understand the shear design of NEXT F beam bridges, this paper conducted a comprehensive parametric study on 48 prestressed concrete NEXT F beam bridges covering various bridge parameters, including concrete strength, beam section, bridge section, and span length. The results of this study tackle the concern of structural safety of NEXT F beam bridges under the increased live load shear.

3 Scope of work

A total of 48 NEXT F beam bridges (non-skewed) were analytically examined with two different bridge sections (i.e., I, II), as illustrated in Fig. 2. Bridge section I consists of four 8 ft wide NEXT beams, while bridge section II consists of four 12 ft wide NEXT beams. For each bridge section, four beam sections (i.e., NEXT 24, NEXT 28, NEXT 32, and NEXT 36) were investigated; for each beam section, two different span lengths and three different types of concrete strengths were examined. The details of the 48 bridges examined herein are summarized in Table 2.

4 AASHTO LRFD shear design

The AASHTO LRFD shear design of prestressed concrete bridges requires the factored shear force at the specified section (V_u) be less than or equal to the factored nominal shear resistance of the section considered (φV_n), in which φ = 0.9 for normal weight concrete and V_n = V_c + V_s + V_p (where V_c, V_s, and V_p are the nominal shear resisted by the concrete, the transverse shear reinforcement, and the component of prestressing force in the shear direction, respectively) [9, 10]. Note that V_p is equal to zero when straight prestressing strands are used [9, 10]. The following Equation (1) shows the expression for V_c, whereas Equation (2) shows the expression for V_s, as provided in [10]: $V_{c} = 0.0316 β \sqrt{f_{c}^{'}} b_{v} d_{v}$ (1) $V_{s} = \frac{A_{v} f_{y} d_{v} (cot θ + cot α) (sin α)}{s}$ (2)

In Equations (1) and (2), $f_{c}^{'}$ is the specified concrete compressive strength of the beam for use in design; b_v is the effective beam web width; d_v is the effective shear depth; α is the angle of inclination of transverse reinforcement to the longitudinal axis of the beam (e.g., α= 90° for vertical shear stirrups); f_y is the specified yield strength of transverse reinforcement; s is the spacing of stirrups; and A_v is the area of transverse reinforcement within the spacing s [9, 10]. Note that the minimum transverse reinforcement (A_v,min) is determined by Equation (3) [10]: $A_{v, min} = 0.0316 \sqrt{f_{c}^{'}} \frac{b_{v} s}{f_{y}}$ (3)

When the beam section contains at least the minimum transverse reinforcement, the following Equations (4 and 5) are used to compute β and θ, respectively, in which ɛ_s is calculated with Equation (6), as shown below [10]: $β = \frac{4.8}{1 + 750 ɛ_{s}}$ (4) $θ = 29 + 3500 ɛ_{s}$ (5) $ɛ_{s} = \frac{\frac{| M_{u} |}{d_{v}} + 0.5 N_{u} + | (V_{u} - V_{p}) | - A_{ps} f_{po}}{(E_{s} A_{s} + E_{p} A_{ps})}$ (6)

In Equation (6), M_u is the factored moment at the specified section; N_u is the applied factored axial force at the specified section; E_s is the modulus of elasticity of reinforcing bars; A_s is the area of nonprestressed tension reinforcement; E_p is the modulus of elasticity of prestressing strands; A_ps is the area of prestressing strands at the tension side of the beam; f_po is taken as 0.7 f_pu [9, 10]. The factored moment and shear include the effects of dead loads and live loads. Tables 3 and 4 show the AASHTO approximation equations for calculating the LLDF for moment and shear, respectively, for types i and k bridge sections [10].

Table 3

AASHTO LRFD LLDF for moment for types i and k bridge cross-sections (Adapted from [10])

		LLDF for moment	Applicability
Exterior beam	One design lane loaded	Lever rule	–1≤d_e≤5.5
	Two or more design lanes loaded	g = e × g_interior	N_b≥4
		$e = 0.77 + (\frac{d_{e}}{9.1})$
Interior beam	One design lane loaded	$0.06 + {(\frac{S}{14})}^{0.4} {(\frac{S}{L})}^{0.3} {(\frac{K_{g}}{12.0 {Lt}_{s}^{3}})}^{0.1}$	3.5≤S≤16.0
	Two or more design lanes loaded	$0.075 + {(\frac{S}{9.5})}^{0.6} {(\frac{S}{L})}^{0.2} {(\frac{K_{g}}{12.0 {Lt}_{s}^{3}})}^{0.1}$	20≤L≤240
			4.5≤t_s≤12.0
			10000≤K_g≤7000000
			N_b≥4

Note: N_b= number of beams; S = beam spacing (ft); L = span length (ft); t_s= depth of concrete slab (in) (Unit conversion: 1 ft = 304.8 mm; 1 in = 25.4 mm).

Table 4

AASHTO LRFD LLDF for shear for types i and k bridge cross-sections (Adapted from [10])

		LLDF for shear	Applicability
Exterior beam	One design lane loaded	Lever rule	–1≤d_e ≤5.5
	Two or more design lanes loaded	g = e × g_interior	N_b≥4
		$e = 0.6 + (\frac{d_{e}}{10})$
Interior beam	One design lane loaded	$0.36 + \frac{S}{25.0}$	3.5≤S ≤16.0
	Two or more design lanes loaded	$0.2 + \frac{S}{12} - {(\frac{S}{35})}^{2.0}$	20≤L ≤240
			4.5≤t_s ≤12.0
			N_b≥4

Note: N_b = number of beams; S = beam spacing (ft); L = span length (ft); t_s = depth of concrete slab (in) (Unit conversion: 1 ft = 304.8 mm; 1 in = 25.4 mm).

5 Shear Design of NEXT F beam bridges

The shear design of a NEXT F beam bridge should be performed through a complete beam design by satisfying the stress limits at transfer, service, and fatigue limit states, and meeting the requirements for moment and shear at the strength limit state; the live load deflection and horizontal interface shear shall be checked as well [9, 10]. Note that the longer span length of each beam section in Table 2 is about the maximum length the bridge can be designed by meeting all requirements above. Figure 3 shows the typical reinforcement details in a NEXT F beam, as illustrated in [4]: the prestressing strands in each stem are spaced at 2 in. on centers with a concrete cover of 2.5 in. at the bottom side of the beam; the diameter of the strands is 0.6 in.; each beam also has four strands (fully tensioned) located 2.5 in. from the top of the beam; all strands are straight (debond up to 25% of strands); No. 4 steel rebars are typically used for shear stirrups, which are extended into the concrete deck to provide horizontal shear resistance [4]. The reinforcement details in [4] were adopted for the bridges examined herein with additional information, as assumed with reference to [4, 9]: the concrete deck has a thickness of 8 in. (including half inch wearing surface) and a compressive strength of 4 ksi; three different concrete strengths for NEXT beams are considered (see Table 2); the future wearing surface has a weight of 25 psf; the barrier has a base width of 18 in. and a weight of 300 lb/ft; seven-wire low-relaxation type prestressing strands are used (specified tensile strength f_pu= 270 ksi); the yield strength of steel rebars (size #4) is 60 ksi [4, 9]. Note that the LRFD approximate estimate of time dependent loss was used in this study [10]. As aforementioned, this study aimed to tackle the concern for shear safety of NEXT F beam bridges due to the increased live load (LL) shear; therefore, both 1.0 and 1.2 times the LRFD LLDF for shear, along with the LRFD LLDF for moment, were used for comparison; the complete design of the 48 NEXT F beam bridges were performed with reference to [4 , 10], after which V_u, V_c, and V_s at the shear critical section were compiled for comparison studies, as disccussed in the next section.

Fig. 3

Typical reinforcement details in a NEXT F beam (Adapted from [4]; Note: 1 in = 25.4 mm).

6 Results and discussion

6.1 V_u and φV_c for exterior and interior beams

Figures 4–6 show the plots of V_u and φV_c (φ= 0.9 for normal weight concrete [9, 10]) for the exterior and interior beams of the 48 bridges with different concrete strengths. In each plot, the Y-axis represents the shear, whereas the X-axis shows the bridges examined (note: each bridge is named by “bridge section - beam section - beam width - span length”). For example, “II-36F-12-75” refers to the bridge having a bridge section “II” with “NEXT 36F” beams; the beam width is “12ft” and the bridge span length is “75ft” (where 1 ft = 304.8 mm). Figure 4 shows the shear for the bridges having a final concrete strength of 6 ksi and an initial concrete strength of 4 ksi (i.e., $f_{c}^{'}$ = 6 ksi; $f_{ci}^{'}$ = 4 ksi), whereas, Figs. 5 and 6 show the shear for the bridges having concrete strengths of ( $f_{c}^{'}$ = 8 ksi; $f_{ci}^{'}$ = 6 ksi) and ( $f_{c}^{'}$ = 10 ksi; $f_{ci}^{'}$ = 8 ksi), respectively. For comparison, two designs were performed for each bridge, namely, one design with the LRFD LLDF for moment and the LRFD LLDF for shear, whereas the other design with the LRFD LLDF for moment and 1.2 times the LFRD LLDF for shear. The figure legends in Figs. 4–6 show the type of shear (e.g., V_u or 0.9V_c) for the exterior and interior beams. For example, “0.9V_c (Ext)” means “0.9V_c” for the exterior beam; “V_u (Ext, with 1.0LLDF)” refers to V_u in the exterior beam calculated with 1.0 LRFD LLDF for shear; “V_u (Int, with 1.2LLDF)” means V_u in the interior beam with 1.2 LRFD LLDF for shear. It was found that the values of V_c are the same from the two designs for each bridge; the values of V_u were increased by approximately 11–15% due to the 20% increase of LL shear. Also, it can be seen from Figs. 4–6 that, for the same beam section, V_u increases as span length increases, however, V_c decreases as span length increases, regardless of beam position (exterior beam or interior beam), bridge section (type I or type II), or concrete strength. Note that the increase of span length reduces the effective shear depth; thus, V_c decreases. This observation implies that shear becomes more critical when the span length of a NEXT F beam bridge increases. In addition, the LRFD specifications require transverse shear reinforcements be provided when V_u > 0.5φ (V_c + V_p), where φ = 0.9 (for normal weight concrete) and V_p = 0 (for straight strands) [9, 10]; thus, if V_u > 0.5φV_c, shear reinforcements shall be used. As can be observed from Figs. 4–6, both “V_u (with 1 . 0LLDF)” and “V_u (with 1.2LLDF)” are greater than 0.5φV_c (i.e., 0.5 times “0.9V_c”) for the exterior and interior beams in all bridges. Therefore, shear reinforcements shall be provided for both designs (i.e., with 1.0 and 1.2 LLDF for shear), by satisfying the following Equation (7) [10]: $\frac{V_{u}}{φ} ⩽ V_{c} + V_{s} + V_{p}$ (7)

Fig. 4

V_u and $0.9 V_{c} (f_{c}^{'} = 6 ksi; f_{ci}^{'} = 4 ksi)$ .

Fig. 5

V_u and $0.9 V_{c} (f_{c}^{'} = 8 ksi; f_{ci}^{'} = 6 ksi)$ .

Fig. 6

V_u and $0.9 V_{c} (f_{c}^{'} = 10 ksi; f_{ci}^{'} = 8 ksi)$ .

Since φ = 0.9 and V_p = 0, Equation (7) can be re-written as Equation (8), as follows: $\frac{V_{u}}{0.9} ⩽ V_{c} + V_{s}$ (8)

V_s can be computed with Equation (2). Note that when vertical shear stirrups are used, α in Equation (2) is equal to 90 degrees [10]. In this study, vertical shear stirrups are assumed; thus, Equation (2) can be reduced to the following Equation (9) [10]: $V_{s} = \frac{A_{v} f_{y} d_{v} (cot θ)}{s}$ (9)

If the minimum transverse reinforcement A_v,min in Equation (3) is used for A_v in Equation (9), the following Equation (10) can be obtained: $V_{s_\min} = 0.0316 \sqrt{f_{c}^{'}} b_{v} d_{v} (cot θ)$ (10)

The value of V_{s_min} is deemed as the shear resistance by the minimum transverse reinforcement. Next, the values of $\frac{Vu}{0.9}$ were compared to V_c + V_s for all bridges, as discussed next.

6.2

\frac{Vu}{0.9}

and V_c + V_s for exterior and interior beams

Figures 7–9 show the plots of $\frac{V_{u}}{0.9}$ and V_c + V_s for the bridges with concrete strengths ( $f_{c}^{'}$ ) of 6 ksi, 8 ksi, and 10 ksi, respectively. Note that the values of V_s in Figs. 7–9 refer to the the shear resistance by the minimum transverse reinforcement as computed from Equation (10). Similar to Figs 4–6, the Y-axis represents the shear, whereas the X-axis shows the bridges examined (note: each bridge is named by “bridge section - beam section - beam width - span length”). The figure legends in Figs. 7–9 show the type of shear (e.g., V_u/0.9 or V_c + V_s) for the exterior and interior beams. For example, “V_c + V_s (Ext)” means the value of “V_c + V_s” for the exterior beam; “V_u/0.9 (Ext, with 1.0LLDF)” refers to the value of “V_u/0.9” for the exterior beam where V_u was determined with 1.0 LRFD LLDF for shear; “V_u/0.9 (Int, with 1.2LLDF)” means the value of “V_u/0.9” for the interior beam where V_u was determined with 1.2 LRFD LLDF for shear. As can be seen from Figs. 7–8, the values of “V_c + V_s” are greater than that of “V_u/0.9” for bridges with ksi and ksi, regardless of beam position, bridge section, beam section, or the LLDF for shear used. For bridges with ksi (see Fig. 9), the values of “V_c + V_s” are greater than that of “V_u/0.9” for all interior beams regardless of bridge section, beam section, or the LLDF for shear used; for the exterior beams, the values of “V_c + V_s” are greater than that of “V_u/0.9” except for the bridge “II-24F-12-58” which has almost identical values of “V_c + V_s” and “V_u/0.9”. Therefore, it can be said that the minimum transverse reinforcements could provide an adequate safety margin for the shear design of NEXT F beam bridges examined herein, even with a factor of 1.2 for the LRFD LLDF for shear.

Fig. 7

$\frac{V_{u}}{0.9}$ and $V_{c} + V_{s} (f_{c}^{'} = 6 ksi; f_{ci}^{'} = 4 ksi)$ .

Fig. 8

$\frac{V_{u}}{0.9}$ and $V_{c} + V_{s} (f_{c}^{'} = 8 ksi; f_{ci}^{'} = 6 ksi)$ .

Fig. 9

$\frac{V_{u}}{0.9}$ and $V_{c} + V_{s} (f_{c}^{'} = 10 ksi; f_{ci}^{'} = 8 ksi)$ .

It is worth mentioning that the shear resistance by the minimum transverse reinforcement was computed with Equation (10) without performing a real design of shear reinforcements. In practice, #4 rebars (see Fig. 3) are typically used for transverse shear reinforcements in NEXT F beam bridges [4]; the bar spacing shall be designed such that all LRFD shear requirements are met, including the minimum transverse reinforcement, the maximum spacing of shear reinforcements, the maximum nominal shear resistance, and horizontal interface shear [9, 10].

7 Conclusions

In this paper, the required transverse shear reinforcements in NEXT F beam bridges were examined by a comprehensive parametric study, which included parameters such as concrete strength, bridge section, beam section, and span length. A total of 48 NEXT F beam bridges were explored. Based the results from this study, the following conclusions can be made:

For a NEXT F beam bridge with a specific beam section and concrete strength, shear becomes more critical when the span length increases.

Transverse shear reinforcements are required for all NEXT F beam bridges examined herein, regardless of whether 1.0 or 1.2 times of the LRFD LLDF for shear is used.

The LRFD minimum transverse reinforcements could provide an adequate safety margin for the shear design of all NEXT F beam bridges examined herein, regardless of whether 1.0 or 1.2 times of the LRFD LLDF for shear is used.

Considering few bridges examined herein have slightly larger or identical values of “V_c + V_s” compared to that of “ $\frac{V_{u}}{0.9}$ ” (with 1.2LLDF), it is recommended that a factor of 1.2 be used for the LRFD LLDF for shear to ensure a safe design of NEXT F beam bridges, even though the minimum transverse reinforcements will be likely to control the shear design.

References

Soliman

, Frangopol

. Life-cycle cost evaluation of conventional and corrosion-resistant steel for bridges. Journal of Bridge Engineering. 2015;20(1):06014005.

Morcous

, Hatami

, Jaber

. A new precast concrete deck system for accelerated bridge construction. Advances in Civil Engineering Materials. 2018;7(3):303–27.

, Li

, Hu

, Shao

, Tang

. Flexural behavior of a fully prefabricated lightweight UHPC bent cap. Journal of Bridge Engineering. 2020;25(10):04020085.

Culmo

, Seraderian

. Development of the northeast extreme tee (NEXT) beam for accelerated bridge construction. PCI Journal. 2010;55(3).

PCI (Precast/Prestressed Concrete Institute). Guidelines for northeast extreme tee beam (NEXT beam). First Edition. PCI Northeast, Belmont, MA, USA, 2012.

Gardner

, Hodgdon

. The first NEXT beam bridge. PCI Journal. 2013;58(1).

Huang

, Davis

. Live load distribution factors for moment in NEXT beam bridges. Journal of Bridge Engineering. 2018;23(3):06017010.

Huang

. Shear live load analysis of NEXT beam bridges for accelerated bridge construction. Bridge Structures. 2021;17(3-4):111–9.

PCI Bridge Design Manual. 3rd Edition, Precast/Prestressed Concrete Institute. Chicago, IL, 2014.

10.

AASHTO LRFD Bridge Design Specifications, 7th Edition (U.S. Customary Units), The American Association of State Highway and Transportation Officials, Washington, D.C., USA, 2014.