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Section 7: Example Problems

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Example Problem 1

Given: A rural two-lane collector highway containing 6 ft [1.8 m] wide shoulders and a current ADT of 500 is illustrated in Figure A-8. The area of concern is a 16 ft [4.9 m] design horizontal clearance that includes 1V:2H side slopes on a 10 ft [3 m] high embankment section that is 125 ft [38 m] in length alongside the highway.

Example 1 Problem Layout Rural Low Volume.
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Figure A-9. Example 1 Problem Layout Rural Low Volume. Click here to see a PDF of the image.

Solution: From the information above and referring to Figure A-1 it is determined that a “rail is needed.” As shown in Figure A-7, the length of need is L = Lu+Lp+Ld. From the given information, Lp = 125 ft [38 m]. Because the ADT is less than 750, Equation A-1 is used to solve for Lu and Ld (if necessary).

For the upstream (westbound traffic) direction, the area of concern is the full (16 ft [4.9 m]) horizontal clearance width and the guardrail offset is 6 ft [1.8 m]. Substituting in Equation A-1.

(US Customary):

(Metric):

Equation A-3

As shown in Equation A-3, a placement of guardrail alongside the 6 ft [1.8 m]-wide shoulder results in Lu = 125 ft [38 m].

Referring to figure A-8, the length of guaradrail needed in the downstream (eastbound traffic) is zero because the offset distance from the edge of the travel lane (centerline marking) to the area of concern is greater than the design horizontal clearance (17 ft [5.1 m] greater than 16 ft [4.9 m]). Therefore, Ld is zero.

The design placement is shown in Figure A-9 including 125 ft [38 m] of guardrail adjacent to the obstacle plus 125 ft [38 m] shielding westbound traffic upstream of the obstacle. These lengths of need do not include end treatments.

Example 1 Problem Solution Guardrail Layout (click in image to see full-size image) Anchor: #i1001860grtop

Figure A-10. Example 1 Problem Solution Guardrail Layout

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Example Problem 2

Given: A rural two-lane arterial highway containing a shoulder width of 8 ft [2.4 m] and a current ADT of 3500 is illustrated in Figure A-10. The areas of concern are bridge bents located 5 ft [1.5 m] from the edge of shoulder. The side slopes are 1V:6H.

Example 2 Problem Layout Rural High Volume. (click in image to see full-size image) Anchor: #i1001870grtop

Figure A-11. Example 2 Problem Layout Rural High Volume.

Solution: Referring to Table A-1: General Applications of Conditions for Roadside Barriers bridge piers within the horizontal clearance (30 ft [9 m] in this case) warrant Guardrail placement for the northside of the roadway displayed in Figure A-10. As shown in Figure A-7 the length of need is L = Lu+Lp+Ld. Therefore, Lp is 34 ft [10.4 m] from the given (see Figure A-10) information. Because the ADT is greater than 750, Equation A-2 is used to find Lu and Ld (if necessary):

(US Customary):

(Metric):

Equation A-4.

Substituting in the equation, the upstream length (Lu) is 116.5 ft [35.5 m] as shown in Equation A-4 if placement is at the shoulder edge.

The downstream (westbound traffic) length of guardrail is also determined by substituting into Equation A-2:

(US Customary):

Metric):

Equation A-5

Substituting in the equation as shown in equation A-5, Ld is 65 ft [19.7 m] as shown in Equation A-5, based on the shoulder edge placement. For westbound traffic, the centerline is the edge of the travel lane and thus guardrail is placed 20 ft [6 m] (12 ft [3.6 m] lane plus 8 ft [2.4 m] shoulder) from the edge of the travel lane.

Total length of guardrail, Lu+Lp+Ld, thus is 116.5 ft [35.5 m] + 34 ft [10.4 m] + 65 ft [19.7 m] or 215.5 ft [62.3 m]; or, rounded to an even length of guardrail, 225 ft [68.6m].

The solution for the south side of the roadway yields the same results, hence placement should be as shown in Figure A-11.

 Example 2 Problem Solution Guardrail Layout.
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Figure A-12. Example 2 Problem Solution Guardrail Layout. Click here to see a PDF of the image.

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Example Problem 3

Given: A divided (76 ft [22.8 m] median) highway with 4 ft [1.2 m] left and 10 ft [3.0 m] right shoulder widths is illustrated in Figure A-12. The median slopes are 1V:10H, and the outside side slopes are 1V:6H. The cross sectional design allows for the addition of a future lane on the median side of the present lanes. The areas of concern are overhead sign bridge supports offset 25 ft [7.6 m] left and 18 ft [5.5 m] right from edge of the travel lanes as shown below. The ADT is 10,000.

Example 3 Problem Layout Divided Highway. (click in image to see full-size image) Anchor: #i1001882grtop

Figure A-13. Example 3 Problem Layout Divided Highway.

Solution: Crash cushions in lieu of guardrail should be considered, particularly for facilities with higher than 10,000 ADT. For this example problem assume crash cushions are not cost effective.

Because the median is sloped at 1V:10H, as shown in Figure A-12, guardrail may be placed thereon (see Figure A-5,). Therefore place the guardrail such that the back of the posts are 5 ft [1.5 m] in front of the median overhead sign bridge support to allow for deflection, i.e., 20 ft [6.0 m] from the edge of the travel lanes (including the 1.5 ft [0.5 m] from the back of the post to the face of the rail).

Referring to Figure A-7, L = Lu+Lp+Ld. For one-way traffic operations, Ld=0; furthermore, for the overhead sign bridge support Lp=0. Equation A-2 is used to find Lu because ADT is greater than 750:

(US Customary):

(Metric):

Equation A-6

For the median side, Lu = 65 ft [20 m] (rounded to 75 ft [22.9 m] to conform to even lengths of guardrail) based on parallel placement for the full length of need, and placement on the 1V:10H slope 5 ft [1.5 m] in front of the fixed object. In contrast, parallel placement at the shoulder edge would have required over 200 ft [60 m] of guardrail.

For the right side of traffic, guardrail must be placed at the shoulder edge (Reference Figure A-5). Substituting in Equation A-2 to determine Lu:

(US Customary):

(Metric):

Equation A-7

Using parallel placement for the entire length, Lu = 111 ft [34.5 m] (which should be rounded to 125 ft [38] to conform to even lengths of guardrail).

Using parallel placement for the entire length of guardrail for both the median and left side, placement is as shown in Figure A-13.

Example 3 Problem Solution Guardrail Layout. (click in image to see full-size image) Anchor: #i1002044grtop

Figure A-14. Example 3 Problem Solution Guardrail Layout.

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