Influence of railings on load carrying capacity of concrete slab bridges

Abstract

This paper presents the results of a parametric study investigating the influence of railings on the load carrying capacity of simply-supported, one-span, multi-lane reinforced concrete slab bridges. A total of 112 bridge cases were modeled using finite element analysis (FEA) subject to AASHTO HS20 truck loadings positioned transversely and longitudinally to produce the maximum bending moments and deflections for cases with and without railings which were compared with AASHTO procedures. Placing two railings on the bridge, AASHTO Standard Specifications procedures overestimated the FEA moments by 100% for one-lane bridges, and by 20% for bridges with two or more lanes. AASHTO LRFD overestimated the FEA moments in all bridge cases by 150% for one-lane, 70% for two-lanes, and a 30% for three- and four-lanes when placing two railings on slab bridges. The results of this study support the AASHTO procedures in designing new concrete slab bridges. However, the paper can also assist engineers in modeling the actual bridge geometry using FEA to account for structural elements such as integral railings in resisting special permit loading on concrete slab bridges.

Keywords

Concrete slab bridges railings multilane bridges finite element analysis AASHTO specifications

1 Introduction

A significant number of highway bridges are short-span reinforced concrete slabs that are owned and maintained by local and state governments. The main advantage of concrete slab bridges is the ease of construction and the ability to field adjustment of the roadway profile during construction. Even though these bridges are designed and built according to national standards over the years, they are generally in good condition and can carry daily traffic. These bridges may not be able to carry modern highway loading or special permit vehicles if not modeled using FEA and account for elements such as railings and sidewalks. Therefore, bridge engineers are expected to perform the load carrying capacity of existing bridges by using either the American Association of State Highway and Transportation Officials (AASHTO) procedures or take advantage of commercial FEA programs to validate and approve those permit vehicles.

The design of highway bridges in the United States conforms to AASHTO Standard Specifications for Highway Bridges (2002) or the AASHTO Load and Resistance Factor Design (LRFD) Bridge Design Specifications (2012) [1, 2]. The analysis and design of any highway bridge must consider live loads such as HS20 (truck or lane) or HL93 (combination of HS truck and lane loading). HS20 design truck loading provision governs short-span structures when considering AASHTO Standard Specifications. To analyze and design reinforced concrete slab bridges, AASHTO specify a bending moment expression or a distribution width for live loading that simplify the two-way bending problem into a beam or one-way bending problem. AASHTO LRFD procedures specify HL93 live load (combination of HS20 trucks or tandem with lane loading) and use distribution width procedures comparable to bending moment expressions specified by AASHTO Standard Specifications. This research builds on published work and previous studies that indicated the equivalent strip width method prescribed by AASHTO, which is widely used for the analysis and design of reinforced concrete slab bridges, to be conservative. The current AASHTO procedures do not consider the effect of railings that are built integrally with bridge deck and its increase in the load-carrying capacity of existing bridges. There were no parametric investigations related to influence of railings on the load carrying capacity of existing bridges reported in the literature search performed before conducting this study. Therefore, this study investigates the presence of railings and the increase in the load-carrying capacity of reinforced concrete slab bridges.

Mabsout et al. (2004) reported the results of a parametric investigation, using finite-element analysis (FEA), of straight, single-span, simply-supported reinforced concrete slab bridges [3]. The study considered various span lengths, slab widths with varied number of lanes, and live loading conditions for bridges, with and/or without shoulders. Longitudinal bending moments and deflections in the concrete slab were evaluated and compared with procedures specified by AASHTO Standard Specifications and LRFD. However, this published research did not consider the effect of railings on the load carrying capacity of concrete slab bridges. The research results indicated that AASHTO Standard Specifications slab moments overestimated the FEA moments by 30% for one lane with span length up to 7.5 m, and the AASHTO slab moments agreed with the FEA moments for spans longer than 8 m. When considering two or more lanes with spans up to 10.5 m, AASHTO slab moments were similar to FEA moments. However, as the span lengths increases, AASHTO slab moments were less than the FEA bending moment by 15 to 30%. The AASHTO LRFD procedure gives higher bending moments than AASHTO Standard Specifications as well as the FEA results.

Davids et al. (2013) reported the development of finite element analysis software designed specifically for the load rating of flat slab bridges [4]. The FEA software formulation and convergence were verified with commercial FEA software. Results of live load tests of an instrumented, in-service flat slab bridge were also reported. The FEA model predicted slab moments that were shown to be conservative relative to the moments inferred from the load test data for a range of truck positions. Fourteen in-service flat slab bridges were load rated with both FEA analysis and the AASHTO equivalent strip method to assess the degree of conservatism inherent in the AASHTO approximate analysis. The FEA results showed an average increase in rating factor of 26% for short-span, two lane flat-slab bridges, when compared with the AASHTO strip width method.

All of the published research had investigated the effect of railings on load distribution factors in either steel girder bridges or prestressed concrete girder bridges. A summary of recent studies published in the literature is presented in this paper for completeness. Mabsout et al. (1997) reported the results of parametric study that investigated the influence of sidewalks and railings on wheel load distribution in steel girder bridges [5]. Typical one-span, two-lane, simply-supported, composite steel girder bridges were selected to investigate the influence of various parameters such as: span length, girder spacing, raised sidewalks, and the addition of railings on live load distribution. The presence of sidewalks and railings was shown to increase the stiffness of the superstructure and improve the load-carrying capacity of steel bridges by as much as 30%. Also, Eamon and Nowak (2002) reported the contribution of bridge stiffening elements such as barriers (railings), sidewalks, and diaphragms on the ultimate capacity and wheel load distribution in composite steel and prestressed concrete girder bridges [6]. Typical secondary elements were shown to reduce girder distribution factors by 10 to 40% depending on the stiffness and bridge geometry. It was also shown that the bridge system ultimate capacity was increased from 1.1 to 2.2 times that of the reference bridge without secondary elements. Chung et al. (2006) conducted a study investigating the influence of secondary elements and deck cracking on the lateral load distribution of steel girder bridges [7]. It was found that the presence of secondary elements such as lateral bracing and railings produces load distribution factors up to 40% lower than the AASHTO LRFD values. Conner and Huo (2006) investigated the effect of railings and bridge aspect ratio on live-load moment distribution in bridge girders [8]. The finite element method was used to investigate 34 two-span continuous bridges with different skew angles and overhang lengths. The presence of railings was shown to reduce distribution factors by as much as 36% and 13% for exterior and interior girders, respectively. Akinci et al. (2008) tested the railing strength and contribution to live-load response for super-load passages [9]. The results of this study showed that girder distribution factors (GDFs) can be decreased by as much as 30%, depending on the stiffness of the girders and the transverse truck position if the parapets or railings were included in the analysis.

This paper presents the results of a parametric study while building on previously published research [3, 5] by investigating the influence of railings on the increase in load carrying capacity of simply-supported, one-span, multi-lane reinforced concrete slab bridges using the finite element method. A total of 112 bridge cases were modeled using FEA subject to static HS20 wheel loading. Various practical bridge parameters investigated in this study were the span length, number of lanes (one to four), with AASHTO HS20 truck loadings positioned transversely and longitudinally to produce the maximum longitudinal live load bending moments. Typical railings were placed on either edge or both edges and assumed to be built integrally with the concrete slabs. The FEA results for cases with railings were compared to the reference bridges without railings as well as with the AASHTO Standard Specifications and LRFD procedures. The results of this parametric investigation can be used by engineers to estimate the load carrying capacity of existing bridges using 3D FEA and issue special load permit. This paper can also be used by other researchers to either investigate other geometric parameters or use the methodology to verify test results.

2 AASHTO bending moments and slab thickness

For simply-supported concrete slab bridges, AASHTO Standard Specifications (2002) suggest three approaches in determining the live-load bending moment but only one procedure is used in this study that was compared with the finite element analysis results. This paper builds on a published parametric investigation reported by Mabsout et al. (2004) and El Meski et al. (2011) that considered empirical moment equation for concrete slabs (AASHTO Section 3.24.3.2) as described below [3, 10].

SI Units: $\begin{matrix} M = 13, 500 S & for S = 15 m (1 a) \\ M = 1, 000 (19 . 5 S - 90) & for S > 15 m (1 b) \end{matrix}$

While U.S. Customary Units, are equivalent to: $\begin{matrix} M = 900 S & for S = 50 ft (2 a) \\ M = 1, 000 (1 . 30 S - 20) & for S > 50 ft (2 b) \end{matrix}$

Where:

S = span length [m for Eq. (1) or ft for Eq. (2)]

M = longitudinal bending moment per unit width [N-m/m for Eq. (1) or lb-ft/ft for Eq.(2)]

AASHTO LRFD Section 4.6.2.3 (2012) provides an equivalent strip width procedure to design reinforced concrete slab bridges that is comparable to procedures specified in the Standard Specifications. AASHTO LRFD Section 3.6.1.2 requires HL93 live loading. This approach is to divide the total bending moment by an equivalent width to obtain a statical design moment per unit width. The equivalent width “E” of longitudinal strips per lane for both shear and moment is determined using the following formulas [2]: Width for one lane loaded is: $E = 250 + 0.42 (L_{1} W_{1})^{1 / 2} (3 a)$

or $E = 10 + 5 (L_{1} W_{1})^{1 / 2} (3 b)$

Width for multi-lanes loaded is: $E = 2, 100 + 0.12 (L_{1} \cdot W_{1})^{1 / 2} (4 a)$

or $E = 84 + 1.44 (L_{1} \cdot W_{1})^{1 / 2} (4 b)$

Where

E = equivalent width of longitudinal strips per lane, mm for Eqs. (3a) and (4a) [inches in Eqs. (3b) and (4b)]

L₁ = span length in mm (ft), the lesser of the actual span or 18,000 mm (60 ft)

W₁ = edge-to-edge width of bridge in mm (ft) taken to be the lesser of the actual width or 18,000 mm (60 ft) for multi-lane loading, or 9,000 mm (30 ft) for single-lane loading

AASHTO Standard Specifications Section 3.24.8 requires edge beams along the free edges of the concrete slab bridges without specifying beam width. The live-load bending moment specified for an edge beam is: 0.1PS (where P = 72 KN or 16 kips for HS20 truck). AASHTO LRFD edge beam moment (Section 4.6.2.1.4b) is assumed to support one line of wheel load and a tributary portion of the design lane load. The effective width is considered to be the sum of the distance between the edge of the deck and the inside face of barrier plus 300 mm (1 ft) and one quarter of the strip width calculated above, but shall not exceed one-half the full strip width or 1.8 m (6 ft).

The concrete slab thicknesses were calculated according to AASHTO Standard Section 8.9.2 or AASHTO LRFD Table 2.5.2.6.3-1 to limit the live-load deflection. The minimum thickness “h” for a concrete slab bridge with main reinforcement parallel to traffic is a function of the span length and defined as: 1.2(S+3,000)/30, where “h” and “S” are in millimeter (or 1.2(S+10)/30, where “h” and “S” are in feet). Furthermore, the AASHTO Standard Section 8.9.3.1 deflection criterion of (S/800) was used to compare with the maximum FEA live-load deflection.

3 Description of bridge cases

Typical simply-supported one-span, one-lane, two-lane, three-, and four-lane reinforced concrete slab bridge cases were analyzed in this investigation. Four single span lengths were considered in this parametric study: 7.2, 10.8, 13.8, and 16.2 m (24, 36, 46, and 54 ft) with corresponding slab thicknesses of 450, 525, 600, and 675 mm (18, 21, 24, and 27 inches), respectively. The concrete slab thicknesses were calculated using the AASHTO equations reported in earlier sections. The overall slab widths were assumed to be: 4.2 m (14 ft) for one lane, 7.2 m (24 ft) for two lanes, 10.8 m (36 ft) for three lanes, and 14.4 m (48 ft) for four lanes. The dimensions and geometric characteristics of the bridges analyzed are also summarized in Table 1. Standard railings were considered to have geometry of 200 millimeter (8 inches) wide and 760 millimeter (30 inches) high above roadway. Bridges without railings were first analyzed and considered as the reference cases. Railings were then placed integrally on one side (left or right) and both sides of the slab edges. The selected monolithic concrete railings are more common due to the multiple purpose of resisting vehicle impact and increase stiffness of the bridge deck and consequently increase the load carrying capacity. Adding concrete railings integrally to the bridge deck might be a way of rehabilitating an existing bridge and improve the load carrying capacity. No other railings were considered in this study due to the minimum stiffness contribution to the bridge. It was decided not to increase the width of two-, three-, and four-lane cases to accommodate any shoulders or sidewalks, which is a conservative assumption. Figures 1 and 2 show typical cross-sections used for two-lane bridge cases with railings, and with centered and edge transverse HS20 wheel loading cases, respectively. The material properties used in modeling the highway bridge cases were normal-strength reinforced concrete. The compressive strength of concrete was 27.5 MPa (4,000 psi), with a modulus of elasticity of 25 GPa (3.6×10⁶ psi), and Poisson’s ratio of 0.2.

Table 1
Dimensions and geometrical characteristics of bridges

Number Slab Width Span Length Slab Thickness

of Lanes (m) (m) (mm)

1 4.2 7.2 450

10.8 525

13.8 600

16.2 675

2 7.2 7.2 450

10.8 525

13.8 600

16.2 675

3 10.8 7.2 450

10.8 525

13.8 600

16.2 675

4 14.4 7.2 450

10.8 525

13.8 600

16.2 675

Number	Slab Width	Span Length	Slab Thickness
1	4.2	7.2	450
		10.8	525
		13.8	600
		16.2	675
2	7.2	7.2	450
		10.8	525
		13.8	600
		16.2	675
3	10.8	7.2	450
		10.8	525
		13.8	600
		16.2	675
4	14.4	7.2	450
		10.8	525
		13.8	600
		16.2	675

Fig.1

Typical cross-sections of two-lane bridge cases with Centered loading condition.

Fig.2

Typical cross-sections of two-lane bridge cases with Edge loading condition.

4 Bridge loading

The bridge cases considered were subjected to AASHTO HS20 design trucks assumed to be traveling in the same direction when considering multiple lanes. The longitudinal location of HS20 axle loads that produce maximum positive moment in one-span bridges was placed such that the centerline of bridge aligned with the location of centerline halfway between the resultant load of the truck and the middle axle. However, a study reported by Mabsout et al. (2004) showed that the difference between placing the middle axle aligned with the mid-span versus the actual location mentioned above was negligible in determining the maximum bending moment in concrete slab bridges [3]. This difference ranged from 0.4% for the 7.2 m (24 ft) span bridge, 2.9% for the 10.8 m (36 ft) span bridge, 1.6% for the 13.8 m (46 ft) span bridge, and 1.1% for the 16.2 m (54 ft) span bridge. Therefore, this simplified approach of placing middle axle wheel loads of HS20 design truck at mid span was adopted in this study.

Two possible transversely loading conditions in each lane were also considered in this study: Centered and Edge loading conditions. Figure 1 shows the Centered loading condition on a two-lane bridge case where each design truck is centered in its own lane. Figure 2 shows the Edge loading condition for the same two-lane bridge case where the first design truck was placed close to one edge (left) of the slab, such that the center of the left wheel of the left most truck is positioned at 0.3 m (1 ft) from the left edge of the slab, and the other trucks were placed side-by-side with a distance 1.2 m (4 ft) between the adjacent trucks in order to produce the worst live loading condition on the bridge. Mabsout el al. (2004) has shown that the Edge loading condition was more critical than the Centered one with/without shoulders and in the absence of concrete railings [3]. Both Centered and Edge loading transverse truck positions are considered in the current study to investigate the effect of railings on live load bending moments and it is effect on increasing the load carrying capacity in concrete slab bridges. Figure 3 presents a typical layout of a two-lane bridge case subjected to HS20 Edge loading.

Fig.3

Typical layout for a two-lane bridge subject to Edge loading condition.

5 Finite element modeling

A total of 112 slab bridge cases were investigated using the FEA. The computer program SAP2000 (2007) was used to discretize the bridge into a convenient number of square four-node shell elements with six degrees of freedom at each node [11]. All elements were assumed to be linearly elastic and the structural analysis assumed small deformations and deflections. The dimensions selected for the shell elements were based on a sensitivity analysis that investigated the appropriate mesh discretization. A comparison was performed for three shell element sizes: 0.15 m×0.15 m (0.5 ft×0.5 ft), 0.3 m×0.3 m (1 ft×1 ft), and 0.6 m×0.6 m (2 ft×2 ft) elements. The FEA results obtained were nearly identical for the three cases. Therefore, the FEA shell element 0.3 m×0.3 m (1 ft×1 ft) was adopted for all the bridge cases modeled in this study. The FEA mesh generated by SAP2000 was also convenient for placing the truck wheel loads at 0.3 m (1 ft) intervals in order to obtain the maximum live load bending moments in the slab bridges. The support conditions for the simply-supported bridges were modeled so that the left and right piers are assigned as hinge and roller supports, respectively.

Referring to Figs. 1 and 2, railings are placed on either edge or both edges of the slab, and are modeled as follows: (a) shell elements placed orthogonally on top and along the edge(s) of each slab which represent a realistic geometric model, or (b) beam elements placed “eccentrically” along the slab edge(s) with the second moment of area calculated about its base. The two FEA railing models gave similar results for longitudinal moments and deflections. Therefore, the simpler eccentric beam element was adopted to model the railings in this study.

Various positions of the HS20 design trucks were investigated, longitudinally and transversely, and their wheel loads were applied as concentrated forces at various nodes to produce the maximum longitudinal live bending moment. The longitudinal live load bending moments and deflections were determined using the FEA results. The computer program SAP2000 was used to generate all the finite element models and contour plots of live load bending moments and deflections. Figure 4 illustrates a typical finite-element model with the corresponding longitudinal bending moment contours for a 10.8 m (36 ft) span, two-lane bridge, in the presence of two railings, and subject to HS20 Edge loading condition.

Fig.4

FEA longitudinal bending moments (KN-m/m) in a 10.8 m (36 ft) span, two-lane bridge, with two railings (R2) subject to Edge loading condition.

6 Finite element analysis results

The FEA results are reported in terms of the maximum longitudinal bending moments, maximum edge beam moments, and maximum live-load deflections at critical locations in the concrete slab bridges. The FEA results for bridges with railings were compared with reference bridge cases without railings as well as with AASHTO Standard Specifications and LRFD procedures.

6.1 FEA results vs. AASHTO

Figure 5 shows sample plots of the FEA longitudinal bending moment at the critical sections for all the two-lane bridge cases in combination with the four span lengths (S) and the various railing configurations (R0 for no railing; R1 for one railing; and R2 for two railings), subject to both Centered (C) and Edge (E) HS20 loading conditions. Figures 6 and 7 show the comparison of bending moment plots for the Centered and Edge loadings, respectively, for all the two-lane bridges with 10.8 m (36 ft) span length, with different railing configurations, along with the AASHTO moments. The maximum FEA longitudinal moments in Figs. 6 and 7 for the concrete slabs was defined as the first peak value occurring after the maximum value at the leftmost edge. It should also be noted that the edge beam moment is taken to be the larger at the two edges in the absence of railings, and at the edge without railing in the case of one railing. The edge beam moment will not be considered in the analysis when two railings are present since this moment will be taken by the railing.

Fig.5

FEA longitudinal bending moments for two-lane bridges for all spans (S), with and without railings (R0, R1, R2), subject to Centered (C) and Edge (E) loading conditions.

Fig.6

FEA longitudinal bending moments for a 10.8 m (36 ft) span, two-lane bridge, with and without railings (R0, R1, R2), subject to Centered (C) loading condition, with AASHTO Specs and LRFD.

Fig.7

FEA longitudinal bending moments for a 10.8 m (36 ft) span, two-lane bridge, with and without railings (R0, R1, R2), subject to Edge (E) loading condition, with AASHTO Specs and LRFD.

The maximum FEA slab moments along the critical sections are tabulated for all bridge cases in Table 2, showing both Centered and Edge loadings as presented in Figs 1 and 2. It was demonstrated from Table 2 that the maximum moments corresponding to the Edge loading are greater than those corresponding to the Centered loading, except in one-lane bridge cases where they are almost equal. It was also confirmed that the maximum moments for one railing right are always greater than the case of one railing left. Table 3 summarizes the increase or decrease in predicting bending moments in the concrete slabs when comparing the maximum FEA with the AASHTO moments for all the bridge cases. Table 4 also summarizes percent increase or decrease of the FEA edge moments as compared to the AASHTO bending moments.

Table 2

FEA maximum slab longitudinal bending moments for centered and edge loading conditions

		FEA Maximum Longitudinal Moments (KN-m/m)
Number	Span	No Railing (R0)		One Railing (R1)			Two Railings (R2)
of Lanes	Length (m)	Centered	Edge	Centered	Edge	Edge	Centered	Edge
					(Railing Left)	(Railing Right)
1	7.2	75.0	74.5	59.6	52.5	62.5	45.0	44.9
	10.8	131.5	131.0	99.9	92.8	102.9	76.2	76.0
	13.8	189.4	188.8	149.1	143.4	151.5	119.4	119.2
	16.2	235.6	235.1	195.0	190.3	196.7	163.4	163.0
2	7.2	84.8	92.2	71.9	72.0	86.6	61.7	66.0
	10.8	151.2	159.0	133.7	123.7	142.0	104.9	111.5
	13.8	218.9	226.6	194.2	186.8	202.9	160.9	169.0
	16.2	273.0	280.6	247.1	243.2	255.5	214.5	223.2
3	7.2	85.1	97.8	83.6	81.0	96.5	71.9	78.1
	10.8	152.3	168.7	145.0	135.8	162.2	119.8	129.5
	13.8	220.6	238.1	208.3	201.5	227.2	177.6	192.4
	16.2	275.0	292.6	261.1	259.8	280.5	230.9	248.8
4	7.2	85.2	100.3	84.9	87.3	100.0	77.6	86.3
	10.8	153.0	175.9	150.0	145.9	173.5	129.7	142.2
	13.8	221.9	248.5	215.8	212.1	243.3	188.4	207.5
	16.2	276.8	304.7	269.1	272.6	298.6	240.8	266.7

Table 3

Comparison of FEA maximum slab longitudinal bending moments and AASHTO moments

		FEA Maximum Longitudinal Moments (KN-m/m) and Percent Difference with AASHTO									AASHTO Moments
Number	Span	No Railing (R0)			One Railing (R1)			Two Railings (R2)			(KN-m/m)
of Lanes	Length (m)	FEA	AASHTO	AASHTO	FEA	AASHTO	AASHTO	FEA	AASHTO	AASHTO	AASHTO	AASHTO
			Specs (%)	LRFD (%)		Specs (%)	LRFD (%)		Specs (%)	LRFD (%)	Specs	LRFD
1	7.2	75.0	30%	69%	62.5	56%	102%	45.0	116%	181%	97.2	126.5
	10.8	131.5	11%	61%	102.9	42%	106%	76.2	91%	179%	145.8	212.4
	13.8	189.4	–2%	49%	151.5	23%	87%	119.4	56%	137%	186.3	283.1
	16.2	235.6	–4%	44%	196.7	15%	72%	163.4	38%	107%	225.9	338.9
2	7.2	92.2	5%	18%	86.6	12%	25%	66.0	47%	64%	97.2	108.5
	10.8	159.0	–8%	29%	142.0	3%	44%	111.5	31%	84%	145.8	205.2
	13.8	226.6	–18%	30%	202.9	–8%	45%	169.0	10%	74%	186.3	293.9
	16.2	280.6	–19%	31%	255.5	–12%	44%	223.2	1%	65%	225.9	367.7
3	7.2	97.8	–1%	4%	96.5	1%	5%	78.1	24%	30%	97.2	101.7
	10.8	168.7	–14%	13%	162.2	–10%	17%	129.5	13%	47%	145.8	190.4
	13.8	238.1	–22%	14%	227.2	–18%	20%	192.4	–3%	41%	186.3	271.8
	16.2	292.6	–23%	19%	280.5	–19%	24%	248.8	–9%	39%	225.9	347.0
4	7.2	100.3	–3%	–4%	100.0	–3%	–3%	86.3	13%	12%	97.2	96.8
	10.8	175.9	–17%	2%	173.5	–16%	4%	142.2	3%	27%	145.8	180.0
	13.8	248.5	–25%	8%	243.3	–23%	11%	207.5	–10%	30%	186.3	269.1
	16.2	304.7	–26%	14%	298.6	–24%	16%	266.7	–15%	30%	225.9	347.0

Table 4

Comparison of FEA edge beam moments and AASHTO moments

		FEA Edge Beam Moments (KN-m/m) and Percent Difference with AASHTO									AASHTO Moments
Number	Span	No Railing (R0)			One Railing (R1)			Two Railings (R2)			(KN-m/m)
of Lanes	Length (m)	FEA	AASHTO	AASHTO	FEA	AASHTO	AASHTO	FEA	AASHTO	AASHTO	AASHTO	AASHTO
			Specs (%)	LRFD (%)		Specs (%)	LRFD (%)		Specs (%)	LRFD (%)	Specs	LRFD
1	7.2	90.2	28%	79%	79.2	45%	104%	42.1	173%	284%	115.2	161.9
	10.8	147.2	17%	101%	119.7	44%	147%	77.5	123%	282%	172.8	296.3
	13.8	205.1	8%	109%	168.3	31%	155%	123.1	80%	249%	221.0	428.9
	16.2	251.4	3%	114%	213.4	21%	152%	168.5	54%	219%	259.2	536.9
2	7.2	104.1	11%	38%	100.2	15%	43%	52.6	119%	172%	115.2	143.2
	10.8	173.3	0%	61%	158.9	9%	76%	105.5	64%	165%	172.8	279.8
	13.8	241.8	–9%	74%	219.9	0%	91%	167.8	32%	151%	221.0	420.7
	16.2	296.0	–12%	83%	272.5	–5%	98%	225.0	15%	140%	259.2	540.2
3	7.2	108.5	6%	27%	107.6	7%	28%	56.4	104%	145%	115.2	138.2
	10.8	182.9	–6%	47%	177.6	–3%	51%	119.0	45%	125%	172.8	268.2
	13.8	254.2	–13%	58%	244.2	–10%	64%	189.5	17%	112%	221.0	401.4
	16.2	309.5	–16%	69%	297.7	–13%	75%	250.3	4%	108%	259.2	521.6
4	7.2	110.3	4%	22%	110.1	5%	22%	57.7	100%	132%	115.2	134.1
	10.8	189.3	–9%	37%	187.4	–8%	38%	125.8	37%	106%	172.8	259.2
	13.8	264.4	–16%	51%	259.9	–15%	54%	202.8	9%	97%	221.0	399.2
	16.2	321.7	–19%	62%	315.7	–18%	65%	267.2	–3%	95%	259.2	521.6

Using Tables 3 and 4, it can be observed that, for bridge cases with no railings, AASHTO Standard Specifications generally tends to give similar results to the FEA slab and edge beam moments, with the exception of one-lane with spans less than 12 m (40 ft) where the AASHTO overestimates FEA moments by about 20%. This is more pronounced with more lanes and longer spans, where AASHTO underestimates FEA moments reaching up to 25% (in slab) and 15% (in edge beam) for three and four lanes with spans greater than 12 m (40 ft). The FEA moments for bridge cases with one railing are similar to the cases with no railings, and therefore almost no reduction in the slab and edge beam moments is observed, with the exception of one-lane bridges where the overestimation by AASHTO reaches 50% in spans less than 12 m (40 ft). When two railings are present in a concrete slab, the FEA slab moments decrease significantly and AASHTO overestimates or gives similar moments in almost all cases, reaching 100% for the one-lane bridges with spans less than 12 m (40 ft), and only slightly underestimates these moments by 15% for four-lane bridges with spans longer than 12 m (40 ft).

Also with reference to Tables 3 and 4, AASHTO LRFD overestimates the FEA slab and edge beam moments in almost all bridge cases with or without railings. AASHTO LRFD gives similar results for slab moments in three- and four-lane bridges with spans less than 12 m (40 ft) with one or no railings. The AASHTO LRFD overestimation is largest with one-lane and for the case with no railings; it averages between 50% (one lane) and 10% (three and four lanes) for slab moments, and between 100% (one lane) and 40% (three and four lanes) for edge beam moments. The presence of one railing adds to the AASHTO LRFD overestimation for one-lane bridges only, up to 100% for slab moments and 125% for edge beam moments. When two railings are present, the AASHTO LRFD overestimation of the FEA slab moments becomes more significant reaching an average high of 150% in one-lane bridges or 30% in three- and four-lane bridges.

The maximum live load deflection near mid-span obtained from FEA results are summarized in Table 5 and compared with the AASHTO deflection criterion of (S/800). As expected, the maximum deflections corresponding to the Edge loading are greater than the deflection due to the HS20 positioned in the Center of each lane. For any given span length and corresponding slab thickness, the maximum live-load deflection results decreased due to the increase in stiffness. The FEA deflection results range between 1/5–1/2 of the AASHTO estimated deflections for bridges with no railings, 1/7–1/2 of the AASHTO deflections for bridges with one railing, and 1/9–1/2 of the AASHTO deflections for bridges with two railings. The difference in deflection between FEA results and AASHTO are higher for bridges with fewer lanes, shorter spans, and the presence of railings. It should be noted that the focus of the paper was on investigating the influence of railings on the load carrying capacity of slab bridges. Deflections were calculated and included for completeness using elastic analysis, with the understanding that cracked sections must be used in calculating actual deflections, thus giving higher values than the deflection calculated using the entire slab thickness. The study reported the relative comparison of the same FEA bridge models with and without railings.

Table 5

Comparison of FEA live-load deflections and AASHTO deflections

		FEA Maximum Slab Deflections (mm)			AASHTO
Number	Span	No Railing	One Railing	Two Railings	Deflection
of Lanes	Length (m)	(R0)	(R1)	(R2)	(mm)
1	7.2	1.7	1.4	0.6	9.0
	10.8	4.5	3.5	2.2	13.5
	13.8	7.3	5.8	4.3	17.3
	16.2	8.8	7.3	5.8	20.3
2	7.2	2.0	1.9	1.0	9.0
	10.8	5.5	4.9	3.2	13.5
	13.8	8.8	7.9	6.1	17.3
	16.2	10.6	9.6	8.1	20.3
3	7.2	2.1	2.1	1.3	9.0
	10.8	5.8	5.6	3.7	13.5
	13.8	9.3	8.9	7.0	17.3
	16.2	11.1	10.6	9.1	20.3
4	7.2	2.2	2.2	1.5	9.0
	10.8	6.1	6.0	4.1	13.5
	13.8	9.8	9.6	7.5	17.3
	16.2	11.6	11.4	9.8	20.3

6.2 FEA results with railings vs. no railing

The maximum slab bending moments, edge beam moments, and maximum deflections are summarized in Table 6 for all bridge cases in terms of ratios of FEA results for cases with (one or two) railings to the corresponding cases without railings. Table 6 shows that the reduction in moments and deflections due to one railing is modest when compared to bridges with two railings, and are most significant for the cases with lesser lanes, irrespective of span length. In particular, the presence of one railing reduces the maximum longitudinal bending moment, maximum edge beam moment, and maximum live-load deflection by about 15% to 20% for one-lane bridges, 10% for two-lane bridges, and leads to insignificant reductions for three- and four-lane bridges, regardless of span length. The presence of two railings reduces the maximum longitudinal slab moment by about 30% to 40% and the maximum live-load deflection by about 35% to 60% in one-lane bridges; this reduction is about 20% to 30% for slab moments and 25% to 50% for deflections in two-lane bridges, and about 15% to 20% for moments 20% to 40% for deflections in three- and four-lane bridges. The results of this parametric study demonstrated that monolithic concrete railings improve the load carrying capacity of concrete slab bridges. This paper can be used by bridge engineers to develop a detailed 3D FEA model of an existing bridge in order to evaluate the load carrying capacity when performing load rating or investigating special permit vehicle. The engineer can model the actual bridge geometry and reduce section properties due to deterioration in the railings and bridge deck.

Table 6
Comparison of FEA results with railings to reference case without railings

Ratio of FEA Results with Railings to Reference Case without Railings

Number Span Maximum Longitudinal Moments Edge Beam Moments Maximum Live-Load Deflections

of Lanes Length (m) No One Two No One Two No One Two

Railing Railing Railings Railing Railing Railings Railing Railing Railings

(R0) (R1) (R2) (R0) (R1) (R2) (R0) (R1) (R2)

1 7.2 1.00 0.83 0.60 1.00 0.88 0.47 1.00 0.83 0.38

10.8 1.00 0.78 0.58 1.00 0.81 0.53 1.00 0.77 0.49

13.8 1.00 0.80 0.63 1.00 0.82 0.60 1.00 0.79 0.58

16.2 1.00 0.83 0.69 1.00 0.85 0.67 1.00 0.83 0.66

2 7.2 1.00 0.94 0.72 1.00 0.96 0.51 1.00 0.95 0.49

10.8 1.00 0.89 0.70 1.00 0.92 0.61 1.00 0.90 0.59

13.8 1.00 0.90 0.75 1.00 0.91 0.69 1.00 0.90 0.69

16.2 1.00 0.91 0.80 1.00 0.92 0.76 1.00 0.91 0.76

3 7.2 1.00 0.99 0.80 1.00 0.99 0.52 1.00 0.99 0.60

10.8 1.00 0.96 0.77 1.00 0.97 0.65 1.00 0.97 0.64

13.8 1.00 0.95 0.81 1.00 0.96 0.75 1.00 0.96 0.75

16.2 1.00 0.96 0.85 1.00 0.96 0.81 1.00 0.96 0.82

4 7.2 1.00 1.00 0.86 1.00 1.00 0.52 1.00 1.00 0.69

10.8 1.00 0.99 0.81 1.00 0.99 0.66 1.00 0.99 0.68

13.8 1.00 0.98 0.84 1.00 0.98 0.77 1.00 0.98 0.77

16.2 1.00 0.98 0.88 1.00 0.98 0.83 1.00 0.98 0.84

		Ratio of FEA Results with Railings to Reference Case without Railings
1	7.2	1.00	0.83	0.60	1.00	0.88	0.47	1.00	0.83	0.38
	10.8	1.00	0.78	0.58	1.00	0.81	0.53	1.00	0.77	0.49
	13.8	1.00	0.80	0.63	1.00	0.82	0.60	1.00	0.79	0.58
	16.2	1.00	0.83	0.69	1.00	0.85	0.67	1.00	0.83	0.66
2	7.2	1.00	0.94	0.72	1.00	0.96	0.51	1.00	0.95	0.49
	10.8	1.00	0.89	0.70	1.00	0.92	0.61	1.00	0.90	0.59
	13.8	1.00	0.90	0.75	1.00	0.91	0.69	1.00	0.90	0.69
	16.2	1.00	0.91	0.80	1.00	0.92	0.76	1.00	0.91	0.76
3	7.2	1.00	0.99	0.80	1.00	0.99	0.52	1.00	0.99	0.60
	10.8	1.00	0.96	0.77	1.00	0.97	0.65	1.00	0.97	0.64
	13.8	1.00	0.95	0.81	1.00	0.96	0.75	1.00	0.96	0.75
	16.2	1.00	0.96	0.85	1.00	0.96	0.81	1.00	0.96	0.82
4	7.2	1.00	1.00	0.86	1.00	1.00	0.52	1.00	1.00	0.69
	10.8	1.00	0.99	0.81	1.00	0.99	0.66	1.00	0.99	0.68
	13.8	1.00	0.98	0.84	1.00	0.98	0.77	1.00	0.98	0.77
	16.2	1.00	0.98	0.88	1.00	0.98	0.83	1.00	0.98	0.84

7 Summary and conclusions

The influence of railings on single-span multi-lane reinforced concrete slab bridges was investigated in this paper. A total of 112 bridge cases were modeled using finite element analysis subject to static HS20 truck wheel loading. The FEA longitudinal bending moments, edge beam moments, and live-load deflections were computed at the critical sections of the bridge cases, and the results for bridges with railings were compared to reference bridges without railings. The reduction in moments and deflections due to one railing was modest when compared to the reduction due to the presence of two railings. The presence of two railings reduced the maximum moments and deflections by 50% in one- and two-lane short-span bridges, to a low of 15% in three- and four-lane long-span bridges. The difference was insignificant for three- and four-lane bridges, regardless of span length, due to the diminishing effect of railing on the stiffness of the bridge. The reduction in moments and deflections is accompanied with an increase in the railing moments which should be designed accordingly and built integrally with deck slabs.

For bridge cases with one or no railings, longer spans, and more than two lanes, the AASHTO Standard Specifications underestimated the FEA slab and edge beam moments by as much as 25%, while it overestimated FEA moments for one-lane, with span length less than 12 m (40 ft), by 20% (no railing) to 50% (one railing). When two railings were present, AASHTO overestimated the FEA moments by 100% for one lane and spans less than 12 m (40 ft), and slightly underestimated these FEA moments by about 15% for four-lane and long bridges. However, the AASHTO LRFD gave similar slab bending moments in three- and four-lane short span bridges, with one or no railings, and overestimated the FEA slab and edge bending moments for all other bridge cases with or without railings. The overestimation is largest for one lane and with no railings, reaching up to 50% for slab moments, and between 100% (one lane) and 40% (three and four lanes) for edge beam moments. The presence of one railing added to the AASHTO overestimation for one-lane bridges only, reaching up to 100% for slab moments and 125% for edge beam moments. When two railings are present, the AASHTO LRFD procedures overestimated the FEA slab moments as much as 150% in one-lane bridges and a 30% in three- and four-lane bridges.

AASHTO Standard Specifications and AASHTO LRFD empirical equations do not account for the presence of concrete railings and are neglected in the design process. Based on the FEA results, it is clearly evident that the presence of railings tends to stiffen the concrete slab and increase the load-carrying capacity of the bridge superstructure, which is most significant in bridges with one- and two-lanes. Therefore, the additional stiffness concrete railings built as a part of the slab can be used to increase the load carrying capacity of a bridge in order to accommodate permit load on the bridge. Therefore, the results of this study can be used by bridge engineers to either adopt the three dimensional finite element model presented in this paper to perform load rating analysis of existing slab bridges or analyze the effect of permit vehicle on the bridge. Finally, railings can also be used to strengthen an existing bridge by incorporating the stiffening influence of concrete railings that are constructed integrally with the bridge deck.

Footnotes

Acknowledgments

This research was supported by a grant from the University Research Board (URB) at the American University of Beirut to whom the authors are indebted and thankful.

References

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Influence of railings on load carrying capacity of concrete slab bridges

Abstract

Keywords

1 Introduction

2 AASHTO bending moments and slab thickness

3 Description of bridge cases

Table 1 Dimensions and geometrical characteristics of bridges Number Slab Width Span Length Slab Thickness of Lanes (m) (m) (mm) 1 4.2 7.2 450 10.8 525 13.8 600 16.2 675 2 7.2 7.2 450 10.8 525 13.8 600 16.2 675 3 10.8 7.2 450 10.8 525 13.8 600 16.2 675 4 14.4 7.2 450 10.8 525 13.8 600 16.2 675

6.1 FEA results vs. AASHTO

Footnotes

Acknowledgments

References