aect480-lecture 26 converters

Lecture 26 – of 11

Lecture 26 – Metric Metric units are used everywhere in the world EXCEPT the USA. It is based on scientific measurements, not the length of a king’s foot or the weight of a chicken.

Metric Conversion Factors Multiply: By: To Obtain:

inches 25.4 millimeters (mm) inches 0.0254 meters (m) feet 304.8 millimeters (mm) feet 0.3048 meters (m)

Length

yards 0.9144 meters (m) in2 645.2 mm2 ft2 92,909 mm2 ft2 0.0929 m2

Area

yd2 0.836 m2 in3 16,387 mm3 ft3 28,317,000 mm3 ft3 0.0283 m3 gallons 0.003785 m3 = 1000 liters

Volume

gallons 3.785 liters Weight pounds 0.454 kilograms (kg)

pounds 4.448 Newtons (N) kips 4448 Newtons (N)

Force

pounds per foot (PLF) 14.594 Newtons per meter (N/m) Lb-In 0.11299 N-m Lb-Ft 1.3559 N-m Kip-Ft 1355.9 N-m Kip-Ft 1.3559 kN-m

Moment

Kip-In 112.99 N-m Unit weight Lb per ft3 (PCF) 0.1571 kN/m3

Lb per in2 (PSI) 6895 Pascals = Pa = N/m2 Lb per in2 (PSI) 6.895 kPa = kilopascals = 1000 Pa Lb per in2 (PSI) 0.0006895 mPa = megapascals = N/mm2 Kips per in2 (KSI) 6895 kPa Kips per in2 (KSI) 6.895 mPa Lb per ft2 (PSF) 47.88 Pa Lb per ft2 (PSF) 0.04788 kPa Kips per ft2 (KSF) 47.88 kPa

Stress (pressure)

Kips per ft2 (KSF) 0.04788 mPa


Example 1 GIVEN: All road construction projects in New York State have drawings with metric measurements. All metric drawings always use units of mm for everything. (Reminder: 1 m = 1000 mm) REQUIRED: Convert 1500 mm as shown on the drawings into feet/inch/sixteenths.

Use the conversion 1 inch = 25.4 mm

Number of inches = inchpermm

mm__4.25

1500

= 59.055118 inches = 48” + 11.055118” = 4’ + 11.055118” = 4’ + 11” + (0.055118 x 16th)

= 4’ + 11” + ths1688.0

1500 mm = 4’-11 "161

Example 2 GIVEN: The x-sectional area of a W30x211 steel beam = 62.0 in2. REQUIRED: Determine the area of the beam in units of mm2.

Use the conversion 1 inch = 25.4 mm

1 inch x 1 inch = 25.4 mm x 25.4 mm

1 in2 = 645.2 mm2 Number of mm2 = 62.0 in2 x 645.2 mm2 per in2 Area = 40,002 mm2


Example 3 GIVEN: The tank below. REQUIRED: How many liters are in the tank?

Use the conversion 1 ft3 = 0.0283 m3 Volume = 1781 ft3(0.0283 m3 per ft3) = 50.4 m3 Volume = 50.4 m3(1000 liters per m3) Volume = 50,400 liters

7’-0”

Dia. = 18’-0”

Vol. = )'7()'18(4

2π

= 1781 ft3 = 1781 ft3(7.48 gals per ft3) Vol. = 13324 gal.


Example 4 GIVEN: An ASTM A325 steel bolt is capable of resisting an allowable shear stress of 30 kips per square inch (KSI) REQUIRED: What is the allowable shear stress for the bolt in units of KPa?

Use the conversions of 1 inch = 25.4 mm 1 Pa = 1 N/m2 1 kPa = 1000 Pa 1 lb = 4.448 N

30 KSI = 2130000

inlb

30 KSI = )0254.0)(0254.0(

)__448.4)(30000(mm

lbperNlb

30 KSI = )00064516.0(

)133440(2mm

N

30 KSI = 206,832,414 N/m2 30 KSI = 206,832,414 Pa 30 KSI = 206,832 kPa


Metric Loads

All metric loads, forces and derivatives of those are in units of Newtons. Below is a sampling of typical minimum design live loads for buildings:

Minimum Uniformly Distributed Live Loads per ASCE 7-02

Occupancy: Pounds per ft2 kN/m2 (soft metric) Assembly area – fixed seats 60 2.87 Assembly area – movable seats 100 4.79 Balconies - residential 60 2.87 Bowling alleys, poolrooms, rec. areas 75 3.59 Dining rooms and restaurants 100 4.79 Gymnasium 100 4.79 Hospital – operating rooms, labs 60 2.87 Hospital – private rooms 40 1.92 Library – reading room 60 2.87 Library – stack rooms 150 7.18 Office 50 2.40 Residential 40 1.92 Schools - classrooms 40 1.92 Stadium - bleachers 100 4.79 Stores – 1st floor retail 100 4.79

Material Properties Unit Weight: Modulus Of Elasticity (E): Yield Stress (fy): Material: Lb/ft3 kN/m3 Kips/in2 kN/mm2 Kips/in2 N/mm2

Steel – A36 490 77.2 29,000 205 36 248 Steel – A992 490 77.2 29,000 205 50 345 Aluminum 170 26.7 10,000 70 28 190 Concrete (4000 psi) 150 23.6 3,600 25.4 - - Wood - SYP 37 5.8 1,600 11.3 6 42 Earth – sandy 100 15.7 - - - - Water 62.4 9.8 - - - -


Metric Dimensions

All metric dimensions are in units of millimeters. Below are a few examples of architectural drawings in metric dimensions:


Example 5 – LRFD Steel Beam Analysis GIVEN: A simply-supported ASTM A992 steel W18x35 beam is loaded as shown (all loads are factored and includes beam weight). Assume the beam is continuously laterally braced. REQUIRED:

1) Determine the maximum factored moment in units of kN-m. 2) Determine the plastic section modulus, Zx of the beam in units

of mm3. 3) Determine the LRFD design moment of the beam φMn in units of

kN-m. 4) Determine if the beam is adequate in moment.

Step 1 - Determine the maximum factored moment in units of kN-m:

Mmax = 8

2Lwu

= 8

)11)(/3( 2mmkN

Mmax = 45.4 kN-m

Step 2 - Determine the plastic section modulus of the beam in units of mm3:

From LRFD properties W18x35 → Zx = 66.5 in3

Zx = 66.5 in3 x ⎟⎠⎞

⎜⎝⎛

inmmx

inmmx

inmm 4.254.254.25

Zx = 1,089,742 mm3

11 m

w = 3 kN/m


Step 3 - Determine the LRFD design moment of the beam φMn in units of kN-m:

From LRFD:

φMn = 0.9FyZx

where: Fy = 345 N/mm2 Zx = 1,089,742 mm3

φMn = 0.9(345 N/mm2)(1,089,742 mm3) = 338,360,000 N-mm

= 338,360,000 N-mm x ⎟⎠⎞

⎜⎝⎛

mmmx

NkN

10001000

φMn = 338.4 kN-m

Step 4 - Determine if the beam is adequate in moment:

Since φMn = 338.4 kN-m > Mmax = 45.4 kN-m → beam is OK

See table above


Example 6 – ACI Concrete Beam Analysis GIVEN: The rectangular concrete beam shown below. All loads are factored and includes beam weight. Use f’c = 25 mPa and 3 – 20 mm diameter bars having fy = 400 mPa. REQUIRED: 1) Determine the ACI 318 factored moment capacity, Mu of the beam in

units of kN-m. 2) Determine the ACI 318 factored moment capacity of the beam in units

of Kip-Feet.

Step 1 – Det. moment capacity Mu in units of kN-m:

Mu = 0.9Asfyd(1 - ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

c

yact

ff

'59.0

ρ)

where: As = 3 bars ⎟⎟⎠

⎞⎜⎜⎝

⎛4

)20( 2mmπ

= 942.5 mm2

ρact = bdAs

= )350)(250(

5.942 2

mmmmmm

= 0.0108

250

350


Mu = 0.9Asfyd(1 - ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

c

yact

ff

'59.0

ρ)

= 0.9(942.5 mm2)(400 N/mm2)(350 mm)(1 - ⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛2

2

/25/400)(0108.0(59.0

mmNmmN )

= 106,640,000 N-mm

= 106,640,000 N-mm x ⎟⎠⎞

⎜⎝⎛

mmmx

NkN

10001000

Mu = 106.6 kN-m

Step 2 – Det. moment capacity Mu in units of Kip-Feet:

Mu = 106.6 kN-m x ⎟⎠⎞

⎜⎝⎛

−−

mkNFeetKip

3559.1

Mu = 78.6 Kip-Feet

See conversion table above

aect480-lecture 26 converters

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