## Section 7: Example Problems

Anchor: #i1005711### 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.

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 = L_{u}+L_{p}+L_{d}.
From the given information, L_{p} = 125 ft [38
m]. Because the ADT is less than 750, Equation A-1 is used to solve
for L_{u} and L_{d }(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 L_{u} =
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, L_{d} 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.

Figure A-10. Example 1 Problem Solution Guardrail Layout

Anchor: #i1005802### 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.

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 = L_{u}+L_{p}+L_{d}.
Therefore, L_{p} 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 L_{u} and L_{d} (if
necessary):

(US Customary):

(Metric):

*Equation A-4.*

Substituting in the equation, the upstream length (L_{u)} 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, L_{d} 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, L_{u}+L_{p}+L_{d},
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.

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

Anchor: #i1005919### 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.

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 = L_{u}+L_{p}+L_{d}.
For one-way traffic operations, L_{d}=0; furthermore,
for the overhead sign bridge support L_{p}=0.
Equation A-2 is used to find L_{u} because ADT
is greater than 750:

(US Customary):

(Metric):

*Equation A-6*

For the median side, L_{u} = 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 L_{u}:

(US Customary):

(Metric):

*Equation A-7*

Using parallel placement for the entire length, L_{u} =
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.

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