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BD 21/01

ASSESSMENT OF HIGHWAY BRIDGE STRUCTURES

Click on the Clause No. for the commentary.

CLAUSE No

SUBJECT

Type HA Loading UDL and KEL

Assessment Loading Example for an R.C. deck

Use of MEXE when fill depth > d

Intermediate Piers in Multispan Masonry Arches

*Problem:*

What is the loaded length when the carriageway is skew to the deck beams?

*Solution:*

It's the distance travelled by a point on a vehicle as it crosses the deck along one notional lane; the start and end of the loaded length are the points at which the beam (or part of the deck) you are considering starts and stops feeling the positive effects of the vehicle (ignoring the length of the vehicle).

This is only true if there is load transfer between the longitudinal deck members. If there is poor transverse distribution or if deck beams are particularly skewed to the carriageway then the deck should be loaded with vehicles from Appendices D & E instead of HA loading (see clause 5.2)

The diagram above illustrates the loaded length for a single span deck, but the magnitude of the skew angle would warrant checking the HA analysis using Annex D & E vehicles. If in doubt then the Annex D & E vehicles should be used.

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__Clause 5.20__ __Assessment Live Loading__

*Problem:*

What is the live load rating of a reinforced concrete bridge deck ?

*Example:*

Carriageway = 6m wide

Deck span = 12m (centre to centre of bearings for a simply supported single span)

Depth of concrete deck = 800mm

Depth of road construction = 250mm

Main longitudinal steel reinforcement = 32mm dia mild steel bars at 125mm centres.

Cover to reinforcement = 35mm

Assess for a metre width of deck :

**BD 21/01**

Cl. 5.6

Table 5.1

Number of notional lanes = 2

Notional lane width (b_{L}) = 6.0 / 2 = 3.0m

Cl. 5.18.

From Table 5.2 with 12m loaded length :

W = 63.6 kN/m (per notional lane)

Knife Edge Load = 120 kN (per notional lane)

Cl. 5.23.

AF = 3.65 / 2.5 = 1.46

Cl. 5.26.

For a metre width of deck :

Adjusted HA UDL : W = 63.6 / (1.46 × 2.5) = 17.42 kN/m

KEL = 120 / (1.46 × 2.5) = 32.88 kN

**Live Load Moment:**

Cl. 3.7.

Table 3.1

γ_{fL} = 1.50 (Ultimate limit state)

Assessment HA loading for a metre width of deck :

W = 1.5 × 17.42 = 26.13 kN/m

KEL = 1.5 × 32.88 = 49.32 kN

Cl. 3.10.

γ_{f3} = 1.1

Maximum mid span Bending Moment with KEL at mid span = M_{ult}

M_{ult} = 1.1 [ (26.13 × 12^{2})/8 + (49.32 × 12)/4 ]

Live Load M_{ult} = 1.1 (470 + 148) = __680 kNm__

__Note: Use of γ _{f3}__

BD 56 & BD 61 - γ

_{f3}is used with the design strength so M

_{ult}would be (470 + 148) =

__618 kNm__.

BD 44 - γ

_{f3}is used with the load effect so M

_{ult}= 1.1 × 618 =

__680 kNm__.

**Dead Load Moment:**

Cl. 4.1.

Table 4.1.

For a metre width of deck :

Concrete UDL : w = 0.8 × 2400 × 9.81 / 1000 = 18.84 kN/m

Depth of Road construction = 250mm

From Note to Table 3.1: surfacing = 100mm

Surfacing UDL : w = 0.1 × 2300(Asphalt) × 9.81 / 1000 = 2.26 kN/m

Therefore fill depth = 250 - 100 = 150mm

Fill UDL : w = 0.15 × 2200(Miscellaneous) × 9.81 / 1000 = 3.24 kN/m

Cl. 3.7.

Table 3.1

Concrete γ_{fL} = 1.15

Surfacing γ_{fL} = 1.75

Fill γ_{fL} = 1.20

Assessment Dead Load w = (1.15 × 18.84) + (1.75 × 2.26) + (1.2 × 3.24)

Assessment Dead Load w = 29.51 kN/m

Cl. 3.10.

γ_{f3} = 1.1

Maximum Dead Load mid span Bending Moment = M_{ult}

M_{ult} = 1.1 (29.51 × 12^{2})/8)

Dead Load M_{ult} = 1.1 (531) = __584 kNm__

**Total Mid Span Bending Moment **= (Dead + Live) Moment

**Total Mid Span Bending Moment **= (584 + 680) = **1264 kNm**

**BD 44/15**

**Capacity of Reinforced Concrete Slab:**

Cl. 5.4.2.

(Cl. 5.3.2)

Effective depth d = 800 - 35 - 32/2 = 749mm

f_{y} = 230 N/mm^{2} (see BD 21/97 cl. 4.4)

f_{cu} = 15 N/mm^{2} (see BD 21/97 cl. 4.7)

From Table 4A :
γ_{ms} = 1.15,
γ_{mc} = 1.50

A_{s} = 6434 mm^{2}/m (32mm bars at 125mm c/c)

z = [1-(0.84 × f_{y} × A_{s} ×
γ_{mc}
) / (
f_{cu} × b × d ×
γ_{ms}
)] × d

z = [1-(0.84 × 230 × 6434 × 1.5) / (15 × 1000 × 749 × 1.15)] × d

z = 0.856 d (less than 0.95d)

M_{u} = (f_{y} / γ_{ms}) × A_{s} × z

M_{u} = (230 / 1.15) × 6434 × 0.856 × 749 × 10^{-6} = **825 kNm/m**

**BD 21/01**

**Live Load Rating:**

Cl. 5.20.

Bending Capacity of Concrete Slab = 825 kNm (per metre width)

Assessment Load Mid Span Moment = 1264 kNm (584 dead + 680 live)

Live Load Capacity of Concrete Slab = 825 - 584 = 241 kNm

Hence Max Allowable K = 241 / 680 = 0.35

Cl. 5.22.

Fig 5/2

Assuming worst condition using Hp category

Loaded length = 12m hence:

** Allowable Reduced Vehicle Load = 3 tonnes**

(Group 2 Fire Engines will be allowed)

Note : The shear effects have to be checked in a similar manner to determine whether shear is more critical than bending.

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*Problem:*

Can MEXE be used when the depth of the fill at the crown is greater than the thickness of the arch barrel?

*Solution:*

Many Authorities accept the MEXE analysis if the depth of fill(h) is made equal to the arch barrel thickness(d), i.e. h+d=2d

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*Problem:*

When is a pier considered to be short and stocky?

*Solution:*

A number of Authorities have adopted a height to width ratio of 2:1 for the upper limit of a stocky pier; the height of the pier being measured between the top of foundations and the arch springing level.

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Last Updated : 25/09/2017

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