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# lever rule for DF for interior girders, 2+ lanes

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## lever rule for DF for interior girders, 2+ lanes

(OP)
I am working on a temporary bridge design.  Although I have done LRFD designs in the past, this is the first with 2 design lanes loaded.  Since the deck is steel grid, the Distribution factors are to be determined using the lever rule.  I understand how to apply this rule to the exterior girders, but I am stumped for the interior girders.  Can someone shed some light?  Where do I assume hinges and take moments?  (or am I on the wrong track already!)  How do I apply the wheel loads of adjacent lanes (what distance between)?  My beam spacing is 5'-0".  My first guess resulted in a DF of 1.0 (essentially the interior beam is carrying half of both trucks).

TIA

### RE: lever rule for DF for interior girders, 2+ lanes

When using the lever rule for interior girders, hinges are assumed to exist in the deck at each girder and simple span distribution is used for each wheel load.

For a 5 ft girder spacing, two lanes loaded and a truck with 6' transverse wheel spacing, the worst case loading with the lever rule would be 1.20 Wheel lines or 60% of the total truck weight going to one girder.

To get this result, you can place the wheel lines as follows:

Option #1:  Wheel line directly over girder, adjacent wheel line (from second truck) 4 ft from said girder. The girder reaction is then 1.0 + (1/5)*1.0 = 1.2

Option #2:  Place one wheel line from Truck #1 2 ft from girder in bay one and place one wheel line from Truck #2 2 ft away from the same girder in bay #2.  The girder reaction is then (3/5)*1.0 + (3/5)*1.0 = 6/5  = 1.2

Compare this to the S/5.5 for concrete decks, which would result in a DF = 0.9 and you will note that the level rule usually provides conservative results.

### RE: lever rule for DF for interior girders, 2+ lanes

I'm out of the office so I don't have the LRFD Code in front of me.

"Where do I assume hinges and take moments?" Under the Standard Specs the lever rule would place a hinge at the first interior girder, treating the deck as a simple beam.

"How do I apply the wheel loads of adjacent lanes (what distance between)?" The wheel lines of a truck are 6' apart; the first wheel line of the adjacent would then be 4' away.

I'm curious, why are you applying two trucks? Are you designing a floorbeam? For a stringer, the truck can be positioned directly it. This would give you the maximum loading, particularly if your stringer spacing is 5'.

How many stringers are there?

### RE: lever rule for DF for interior girders, 2+ lanes

(OP)
TTK:  Thanks for your reply.  It seems I was on the right track but hadn't place the trucks properly to get the maximum DF (I was unaware of the 4' between the lanes).  Unfortunately this is bad news for my design/analysis as it seems my bearing stiffeners are inadequate.

bridgebuster: I was applying two trucks b/c the bridge is wide enough to accommodate 2 lanes of traffic which affects the DF of my interior beams.  Since my beam spacing is less than the wheel spacing on a truck, the controlling scenario is adjacent trucks spaced at the 4' between lanes.  There are 5 beams.

### RE: lever rule for DF for interior girders, 2+ lanes

(OP)
TTK:  I have a steel grid deck.  Do you know the ratio for the S/ for steel grid? I was curious as to the comparison with 1.2.  Thanks again

### RE: lever rule for DF for interior girders, 2+ lanes

(OP)
TTK: One more thing...The 1.2 DF is for shear, correct?  There would be a different placement to figure moment - One wheel from each lane spaced 1/2 between adjacent beams to get a maximum moment.

### RE: lever rule for DF for interior girders, 2+ lanes

The AASHTO Standard Specifications for Bridges (STD) suggests WHEEL LOAD distribution factors of S/4.0 and S/5.0 depending on the thickness of the non-composite steel grid deck.  These distribution factors are for moments in interior beams for bridges with two or more design lanes.

The AASHTO LRFD Bridge Design Specifications (LRFD) provides TRUCK LOAD distribution factors of S/8.0 and S/10.0 depending on the thickness of the non-composite steel grid deck.  These distribution factors are also for moments in interior beams for bridges with two or more design lanes.

You will note the two specifications provide the same results since one is a WHEEL load distribution factor and the other is a TRUCK load distribution factor.

The net live load effect is greater for the LRFD, however, since you must consider the uniform design lane load TOGTHER with either the design truck or the design tandem.

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