## 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 clear zone 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.

*Solution: *From the information above
and referring to
Figure
A-1 it is determined that a “rail is needed.” As shown in
Equation A-5, the length of need is L_{total} =
L_{u}+L_{p}+L_{d}.
From the given information, L_{p} = 125 ft [38
m]. Because the ADT is less than 750, Equations A-1 and A-2 are
used to solve for L_{u} and L_{d },
respectively (if necessary).

For the upstream direction, the area of concern is the full
(16 ft [4.9 m]) clear zone width and the guard fence offset (G_{u})
is 6 ft [1.8 m]. Substituting in Equation A-1.

(US Customary):

A placement of guard fence alongside the 6 ft [1.8 m]-wide
shoulder results in L_{u} = 125 ft [38 m].

Referring to figure A-9, the length of guard fence needed
in the downstream 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 clear zone (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-10 including 125 ft [38 m] of guard fence adjacent to the obstacle plus 125 ft [38 m] shielding traffic adjacent to proposed guard fence upstream of the obstacle. These lengths of need do not include end treatments.

Figure A-10. Example 1 Problem Solution Guard Fence 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-11. 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 clear zone (30 ft [9 m] in this case) indicates
guard fence placement for the north side of the roadway displayed
in Figure A-11. As shown in Equation A-5 the length of need is L_{total} =
L_{u}+L_{p}+L_{d}.
Therefore, L_{p} is 34 ft [10.4 m] from the
given (see Figure A-11) information. Because the ADT is greater
than 750, Equations A-3 and A-4 are used to find L_{u} and
L_{d} (if necessary), respectively:

(US Customary):

Substituting in the equation, the upstream length (L_{u})
is 116.5 ft [35.5 m] if placement is at the shoulder edge.

The downstream (westbound traffic) length of guard fence is also determined by substituting into Equation A-4:

(US Customary):

L_{d} is 65 ft [19.8 m]
as shown above, based on the shoulder edge placement. For westbound
traffic, the centerline is the edge of the travel lane and thus
guard fence offset (G) is 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 guard fence, 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 [65.7 m]; or, rounded to an even length
of guard fence, 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-12.

Figure A-12. Example 2 Problem Solution Guard fence Layout.

Anchor: #i1005919### Example Problem 3

*Given*: A divided (76 ft [23.2
m] median) highway with 4 ft [1.2 m] left and 10 ft [3.0
m] right shoulder widths is illustrated in Figure A-13. 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 guard
fence 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-13, guard fence may be placed thereon (see Figure A-5,). Therefore place the guard fence 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 Equation A-5, L_{total} =
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-3 is used to find L_{u} because ADT is greater than
750:

(US Customary):

*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 guard
fence) 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 guard fence.

For the right side of traffic, guard fence must be placed
at the shoulder edge (Reference
Figure
A-5). Substituting in Equation A-3 to determine L_{u}:

(US Customary):

*Equation A-7*

Using parallel placement for the entire length, L_{u} =
111 ft [34 m] (which should be rounded to 125 ft
[38] to conform to even lengths of guard fence).

Using parallel placement for the entire length of guard fence for both the median and left side, placement is as shown in Figure A-14.

Figure A-14. Example 3 Problem Solution Guard Fence Layout.