Part I - Appendix

APPENDIX A - ENGLISH/METRIC CONVERSION FACTORS

AA.1 - Lengths

Symbol	When You Know	Multiply by	To Find	Symbol
	mils	0.254	millimeters	mm
in	inches	25.4	millimeters	mm
ft	feet	0.348	meters	m
yd	yards	0.914 4	meters	m
mi	miles	1.609 347	kilometers	km

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AA.2 - Areas

Symbol	When You Know	Multiply by	To Find	Symbol
in2	square inches	645.16	square millimeters	mm2
ft2	square feet	0.092 903	square meters	m2
yd2	square yards	0.836 127 4	square meters	m2
ac	acres	0.404 687	hectares	ha
mi2	square miles	2.59	square kilometers	km2

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AA.3 - Volumes

Symbol	When You Know	Multiply by	To Find	Symbol
fl oz	fluid ounces	29.573 53	milliliters	mL
gal	gallons (US liquid)	3.785 412	liters	L
ft3	cubic feet	0.028 316 85	cubic meters	m3
yd3	cubic yards	0.764 549	cubic meters	m3

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AA.3 - Mass

Symbol	When You Know	Multiply by	To Find	Symbol
oz	ounces	28.349 52	grams	g
lbs	pounds	0.453 592	kilograms	kg
T	tons (short) (2000 lb)	0.907 184	metric tons	t

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AA.4 - Miscellaneous

Symbol	When You Know	Multiply by	To Find	Symbol
°C	Celsius temperature	$\frac{9(\text{°C})}{5}+32$	Fahrenheit temperature	°F
°F	Fahrenheit temperature	$\frac{5(\text{°F}-32)}{9}$	Celsius temperature	°C
∆°F	change in Fahrenheit	$\frac{5({\Delta }^{\circ }\text{F})}{9}$	change in Celsius	∆°C
psi	pounds per square inch	6 894.757	pascals	Pa

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AA.5 - Metric Prefixes

Multiplication Factor	Prefix	Symbol
1 000 000 000 000 000 000 = 1018	exa	E
1 000 000 000 000 000 = 1015	peta	P
1 000 000 000 000 = 1012	tera	T
1 000 000 000 = 109	giga	G
1 000 000 = 106	mega	M
1 000 = 103	kilo	k
100 = 102	hecto	h
10 = 101	deka	da
1 = 100	base unit	base unit
0.1 = 10-1	deca	d
0.01 = 10-2	centi	c
0.001 = 10-3	milli	m
0.000 001 = 10-6	micro	μ
0.000 000 001 = 10-9	nano	n
0.000 000 000 001 = 10-12	pico	p
0.000 000 000 000 001 = 10-15	femto	f
0.000 000 000 000 000 001 = 10-18	atto	a

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APPENDIX B - GEOMETRIC AND TRIGONOMETRIC REFERENCE CHARTS

The charts in this section contain a number of formulas for performing geometric and trigonometric calculations. These charts should be used as references in calculating quantities for measurement and payment.

AB.1 - Areas of Common Shapes

Shape	Image	Formula
Triangle		$A=\frac{base\times height}{2}$
Square		$A=s^2$
Rectangle		$A=L\times W$
Trapezoid	frameles	$A=\frac{b_1+b_2}{2}h$
Trapezium		$A=\frac{b(h_1+h_2)+a{h}_1+c{h}_2}{2}$
Regular Polygon		$A=\frac{SumofSides\times r}{2}$
Circle	Circle with Radius and Diameter defined	$A=\pi r^2=\frac{\pi d^2}{4}$ $P=2\pi r=\pi d$
Sector	Circle with Radius and Angle for Sector	$A=\frac{\pi r^2\times \Delta }{360^{\circ }}$
Segment of a Circle		When the radius and angle are known (preferred) $A=\frac{r^2(\frac{\Delta \pi }{180}-\sin \Delta )}{2}$ When only the chord and middle ordinate are known, if the Middle Ordinate, a, is less than $\frac{1}{4}$ the Chord b $A\approx \frac{2}{3}ab$ if the Middle Ordinate, a, is greater than $\frac{1}{4}$ the Chord b $A\approx \frac{\pi ab}{4}$
Ellipse	Image of an ellipse with semi-minor axis "a" and semi-major axis "b"	$A=\pi ab$

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AB.2 - Surface Areas and Volumes of Solids

Shape	Image	Surface Area Formula	Volume Formula
Cube		$SA=6\times s^2$	$V=s^3$
Right Cylinder		$SA=2\pi rh$	$V=\pi r^{2}h$
Oblique Cylinder		$SA=2\pi rL$	$V=\pi r^{2}L$
Cone		$SA=\frac{2\pi r\times L}{2}$	$V=\frac{\pi r^{2}h}{3}$
Pyramid		$SA=\frac{Perimeter\times L}{2}$	$V=\frac{AreaofBase\times h}{3}$
Sphere		$SA=4\pi r^2$	$V=\frac{4\pi r^3}{3}$

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AB.3 - Irregular Figures

Shape	Image	Formula
Irregular Polygon		$A=x(\frac{a}{2}+b+c+d+e+f+g+h+\frac{i}{2})$ (Average End Area Formula)
Irregular Volume		$V=x(\frac{\text{CS Area }A}{2}+\mathrm{...}+\text{CS Area }n+\mathrm{...}+\frac{\text{CS Area }Z}{2})$
Parabola		$\text{Area}\approx \frac{2Bh}{3}$

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AB.4 - Triangles and Trigonometry

Right Angled Triangles

$(\mathrm{\angle }\varphi =90^{\circ })$

$a^2=c^2-b^2$ $b^2=c^2-a^2$ $c^2=a^2+b^2$

Known	Needed
	$𝜽$	$𝜷$	$a$	$b$	$c$	Area
$a,b,\varphi$	${\tan }^{-1}\left(\frac{a}{b}\right)$	${\tan }^{-1}\left(\frac{b}{a}\right)$			$\sqrt{a^2+b^2}$	$\frac{a\times b}{2}$
$a,c,\varphi$	${\sin }^{-1}\left(\frac{a}{c}\right)$	${\cos }^{-1}\left(\frac{a}{c}\right)$		$\sqrt{c^2-a^2}$		$\frac{a\sqrt{a^2+b^2}}{2}$
$\theta ,a,\varphi$		$90^{\circ }-\theta$			$\frac{a}{\sin \theta }$	$\frac{a^2}{2\tan \theta }$
$\theta ,b,\varphi$		$90^{\circ }-\theta$	$b\tan \theta$		$\frac{b}{\cos \theta }$	$\frac{b^2\tan \alpha }{2}$
$\theta ,c,\varphi$		$90^{\circ }-\theta$	$c\sin \theta$	$c\cos \theta$		$\frac{c^2\sin (2\theta )}{4}$

Oblique Angled Triangles

$(\mathrm{\angle }\beta >90^{\circ })$

$a^2=b^2+c^2-2bc\cos \theta$
$b^2=a^2+c^2-2ac\cos \beta$
$c^2=a^2+b^2-2ab\cos \varphi$
$s=\left(\frac{a+b+c}{2}\right)$

Known	Needed
	$𝜽$	$𝜷$	$𝝓$	$b$	$c$	Area
$a,b,c$	${\cos }^{-1}\left(\frac{b^2+c^2-a^2}{2bc}\right)$	${\cos }^{-1}\left(\frac{a^2+b^2-c^2}{2ac}\right)$	$={\cos }^{-1}\left(\frac{a^2+b^2-c^2}{2ab}\right)$			$\sqrt{s(s-a)(s-b)(s-c)}$
$a,\theta ,\beta$			$180^{\circ }-(\theta +\beta )$	$\frac{a\sin \beta }{\sin \theta }$	$\frac{a\sin \varphi }{\sin \theta }$
$a,b,\theta$		${\sin }^{-1}\left(\frac{b\sin \theta }{a}\right)$			$\frac{b\sin \varphi }{\sin \beta }$
$a,b,\varphi$	${\tan }^{-1}\left(\frac{a\sin \varphi }{b-a\cos \varphi }\right)$				$\sqrt{a^2+b^2-2ab\cos \varphi }$	$\frac{ab\sin \varphi }{2}$

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APPENDIX C - Steel Shapes and Reinforcement

AC.1 - Structural Steel Shapes

Structural Steel is typically designated by specific marks that correspond to a shape, cross sectional dimension, and sometimes weight as shown in the examples below. Construction staff may encounter them and should either be familiar with the shapes, or familiar with where to look to understand the designations and what they indicate.

Mark	Shape	First Digit	Second Digit	Third Digit	Common Application
$\text{W6 x 9}$	Wide Flange I Beam	Height in Inches	Weight in pounds per foot	n/a	Standard Guardrail Post
$\text{L4 x 3 x }\frac{3}{4}$	Angle	Height in Inches	Width in Inches	Thickness in Inches	Curb/Sidewalk Opening

A full list of all standard structural steel shapes is available at the AISC website. A current version is available for download here: AISC Shapes Database

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AC.2 - Reinforcing Steel

Below is a chart of ASTM Standard Reinforcing Bar sizes and dimensions. These are to be used in calculating Source Document quantities. Reinforcing steel sizing can be easily understood as being divided by eight. i.e. #4 bar is 4/8" = 1/2".

Bar Size Designation	Area (in.²)	Weight (lb/ft)	Diameter (in.)
#3	0.11	0.376	0.375
#4	0.20	0.668	0.500
#5	0.31	1.043	0.625
#6	0.44	1.502	0.750
#7	0.60	2.044	0.875
#8	0.79	2.670	1.000
#9	1.00	3.400	1.128
#10	1.27	4.303	1.270
#11	1.56	5.313	1.410
#14	2.25	7.65	1.693
#18	4.00	13.60	2.257

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AC.3 - Steel Mesh

Welded wire fabric is designated by four components: two numbers representing the spacing of longitudinal and transverse wires and two letter-number combinations representing the type and size of longitudinal and transverse wires.

For example, in “6 x 8 — W8.0 x W4.0”

6 is the spacing of longitudinal wires, in inches

8 is the spacing of transverse wires, in inches

W indicates smooth wire (with D indicating deformed)

8.0 indicates a 0.08 square inch cross-sectional area (longitudinal)

4.0 indicates a 0.04 square inch cross-sectional area (transverse).

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APPENDIX D - FEDERAL HIGHWAY ADMINISTRATION

This appendix contains information specific to the Federal Highway Administration (FHWA) and Federal-aid programs and projects. Included are: the Delaware Department of Transportation/Federal Highway Administration Stewardship Agreement (which includes the Memorandum of Agreement, Construction Contract Change Approval Requirements for Federal- Aid Oversight Projects); and a list of requested notification of FHWA for projects with federal oversight.

Change Order MOA between FHWA & DelDOT

• Stewardship & Oversight Agreement between FHWA & DelDOT

Accessible Design (ADA) – FHWA’s Resource Library for everything related to the Americans with Disabilities Act guidance, policy and related information.

• https://www.fhwa.dot.gov/accessibility/

Buy America – Includes Q’s/A’s

• https://www.fhwa.dot.gov/construction/cqit/buyam.cfm

Construction Program Guide - Intended to provide fast, easy access to Federal-aid construction program regulations, policy, guidance, and training. All construction related information is consolidated under key subject areas, with links to related information. The web site provides a consolidated source for Federal and State construction personnel to find updated information about FHWA's construction program.

• https://www.fhwa.dot.gov/construction/cqit/

Construction Program Management and Inspection Guide, August 2004

• https://www.fhwa.dot.gov/construction/cpmi04tc.cfm

Contract Administration Core Curriculum Manual

• https://www.fhwa.dot.gov/programadmin/contracts/coretoc.cfm

Consultant Services – Includes Q’s/A’s

• https://www.fhwa.dot.gov/programadmin/consultant.cfm

Emergency Relief (ER) Program

• https://www.fhwa.dot.gov/programadmin/erelief.cfm

Employment of Consultants

• https://highways.dot.gov/fed-aid-essentials/videos/other-programs/using-consultants-consultant-services-overview

Federal-Aid Policy Guide (FAPG) - Federal Highway Administration's (FHWA's) current policies, regulations and nonregulatory procedural guidance information (if available) related to the Federal-aid Highway Program.

• https://www.fhwa.dot.gov/federalaid/projects.cfm

Federal-Aid Program Administration

• https://www.fhwa.dot.gov/specialfunding/

FHWA Directives and Memorandums – A directive is a written communication that prescribes or establishes policy, organization, methods, procedures, requirements, guidelines, or delegations of authority. It also provides information essential to the administration or operation of the FHWA. All directives are written in plain language according to the general writing and formatting guidelines in the FHWA Directives Guide below.

• https://highways.dot.gov/laws-regulations/fhwa-directives-guide
• https://highways.dot.gov/laws-regulations/directives

Financing Federal-Aid Highways

• https://www.fhwa.dot.gov/policy/olsp/fundingfederalaid/

Guide to Federal-Aid Programs and Projects

• https://www.fhwa.dot.gov/federalaid/projects.cfm

Highway Related Statutes

• Title 23, United States Code (U.S.C.), Highways
• Title 49, United States Code (U.S.C.), Transportation

Highway Related Regulations

• Title 23, Code of Federal Regulations (CFR), Highways
• Title 49, Code of Federal Regulations (CFR), Transportation

LPA's Federal-Aid Essentials

• https://highways.dot.gov/fed-aid-essentials/federal-aid-essentials-local-public-agencies

Local Public Agency (LPA)

• https://www.fhwa.dot.gov/federalaid/lpa/index.cfm

Major Projects

• https://www.fhwa.dot.gov/majorprojects/

NHI - National Highway Institute - Your source for training the transportation community.

• https://www.nhi.fhwa.dot.gov/home.aspx

OIG - Office of the Inspector General Hotline – If you suspect bid rigging or fraud has occurred in any project funded by FHWA.

• https://www.oig.dot.gov/hotline

Patented and Proprietary Products – Q’s/A’s

• https://www.fhwa.dot.gov/programadmin/contracts/011106qa.cfm

Responsible Charge

• https://www.fhwa.dot.gov/federalaid/110804.cfm

FHWA Websites

• Planning: https://www.fhwa.dot.gov/environment/index.cfm
• Environment: https://www.fhwa.dot.gov/environment/index.cfm
• Right of Way (Realty): https://www.fhwa.dot.gov/real_estate/index.cfm
• Design: https://www.fhwa.dot.gov/design/
• Contract Administration: https://www.fhwa.dot.gov/programadmin/contracts/
• Construction: https://www.fhwa.dot.gov/construction/

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Appendix E - Historical References

Previous reference materials will be maintained here for historical record keeping only.

AE.1 - References from 2002 Construction Manual

Please be advised that these reference materials print exponents in extremely tiny font, which may lead to errors. There is also at least one error contained within the forms. Despite this, they still provide some additional information to inspections staff and are included for historical reference only. Please verify any formulas contained within before utilizing them.

• Downloadable English/Metric Conversion Factor Chart
• Geometric and Trigonometric Reference Chart

AE.2 - Miscellaneous

Previous Inspector Manual circa 2016

• Inspector Manual

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