FORMULAS USEFUL IN CALCULATING WEIGHT OF CASTINGS

Transcription

1 FORMULAS USEFUL IN CALCULATING WEIGHT OF CASTINGS Rectangle and Parallelogram Area = ab Area = ½ cd. Triangle Area = s (s a) (s b) (s c) when s = ½ (a + b + c) Example: a = 3, b = 4, c = 5 3" + 4" + 5" s = = 6" Area = 6 (6 3) (6 4) (6-5) = 6 sq in. Regular Polygons n = Number of sides, s = Length of one side, r = Inside radius Area = ½ nsr Number of Sides Area s² = r² s² = r² s² = r² s² = r² s² = r² s² = 3.49 r² s² = r² s² = r² Trapezium Area = ½ [a (e + d) + bd + ce] Example: a = 10, b = 3, c = 5, d = 6, e = 8 Area = ½ [10 (8 + 6) + (3 6) + (5 8)] = 99 sq. in. 7-1

2 FORMULAS USEFUL IN CALCULATING WEIGHT OF CASTINGS Segment of a Circle Area = R è C (R h) (5.5) Area = = sq. in. 360 Example: R = 5, = 10, C = 8.66, h =.5 Length of arc L = R Area = ½ [LR C (R h)] Example: R = 5, C = 8.66, h =.5, θ = 10 L = = Area = ½ [( ) 8.66 (5.5)] = sq. in. Spandrel Area = R² = C² Example: R = 3 Area = ² = Parabolic Segment Area = ⅔ sh Example: s = 3, h = 4 Area = ⅔ 3 4 = 8 Ellipse Area = πab = ab Example: a = 3, b = 4 Area = = Ring of Circular Cross Section Area of Surface = 4π² Rr = Rr Area of Surface = π² Dd = Dd Volume = π² Rr² = Rr² Volume = ¼ π²dd² =.4674 Dd² 7-

3 FORMULAS USEFUL IN CALCULATING WEIGHT OF CASTINGS Pyramid A = area of base P = perimeter of base Lateral Area = ½ Ps Volume = ⅓ Ah Frustum of a Pyramid A = area of base a = area of top m = area of midsection P = perimeter of base p = perimeter of top Lateral Area = ½ s (P + p) Volume = 1 3 h (a + A + Volume = h (A + a + 4 m) aa ) Cone Volume = ⅓ πr²h = r²h = d²h Conical Area = rs = r r + h Frustum of a Cone A = area of base a = area of top m = area of midsection R = D ; r = d Area of Conical Surface = ½ πs (D + d) = s (D + d) Volume = ⅓ h (R² + Rr + r²) = h (R² + Rr + r²) 1 Volume = 1 h(d² + Dd + d²) = h (D² + Dd + d²) Volume = 1 h (a A aa ) = 6 h (a + A + 4 m) 7-3

4 FORMULAS USEFUL IN CALCULATING WEIGHT OF CASTINGS Sphere Surface = 4 πr = r = πd Volume = πr3 = r3 Volume = πd3 = d3 Segment of a Sphere Spherical Surface = πrh = ¼ π (c + 4 h) = (c + 4 h) Total Surface = ¼ π (c + 8 rh) = (c + 8 rh) Volume = ⅓ π h (3 r - h) = h (3 r - h) or Volume = πh (3 c + 4 h) = h (3 c + 4 h) Sector of a Sphere Total Surface = ½ πr (4 h + c) = r (4 h + c) Volume = ⅔ πrh =.0944 rh Cylinder Cylindrical Surface = πdh = πrh = 6.83 rh Total Surface = πr (r + h) = 6.83 r (r + h) Volume = πrh = ¼ πdh = dh 7-4

5 FORMULAS USEFUL IN CALCULATING WEIGHT OF CASTINGS Circle θ (the Greek letter Theta) = angle included between radii π (pi) = , D = Diameter, R = Radius, C = Chord, h = Height of Arc, L = Length of Arc. Circumfere nce = D = = Area Diameter = R = Circumference = 1 = Radius = D = Circumference C + h Radius = h Area = ¼ πd = D = π R Chord = h (D - h) = R sine? Circle Ring Area = (D-d), or (D-d) (D + d) Example: D = 10, d = 3 Area = (10-3) = sq. in. Sector of a Circle Area = ½ LR Example: L = 10.47, R = 5 θ Area Area C Height of Arc, h = R R è Length of Arc, L = πr = L è ( in degrees) = R C Sine 1 è = R Area = 5 = sq. in. or Area = R è = R è 360 Example: R = 5, θ = 10 Rè 10 Area = = sq. in. 7-5

6 ENGLISH/METRIC (SI) STRESS CONVERSION FACTORS Look up stress to be converted in the boldface column. If in ksi (103 psi), read MPa in righthand column. If in MPa, read ksi in lefthand column. Conversion factors: 1 MPa = 1 MN/m (meganewton per square metre) or 1 N/mm (newton per square millimetre); 1 MPa = ksi, and 1 ksi = MPa. To convert ksi or MPa values above 400, use the supplemental table. Example: Convert 130 MPa to ksi. Solution: 1000 MPa = ksi (from the small table), and 30 MPa = ksi (from the large table). Then, = = ksi. 0 to 100 ksi MPa ksi MPa

7 ENGLISH/METRIC (SI) STRESS CONVERSION FACTORS 100 to 00 ksi MPa ksi MPa to 300 ksi MPa ksi MPa

8 ENGLISH/METRIC (SI) STRESS CONVERSION FACTORS 300 to 400 ksi MPa ksi MPa , to 5000 ksi MPa Source: Anton des. Brasunas. University of Missouri-Rolla MID-JUNE 1979 METAL PROGRESS 7-8

9 TEMPERATURE CONVERSION read known temperatures in bold face and corresponding temperatures in degrees fahrenheit will be found in the column to the left temperatures in celsius (centigrade) to the right F C F C F C

10 TEMPERATURE CONVERSION read known temperatures in bold face and corresponding temperatures in degrees fahrenheit will be found in the column to the left temperatures in celsius (centigrade) to the right F C F C F C ± ±

11 TEMPERATURE CONVERSION read known temperatures in bold face and corresponding temperatures in degrees fahrenheit will be found in the column to the left temperatures in celsius (centigrade) to the right F C F C F C

12 TEMPERATURE CONVERSION read known temperatures in bold face and corresponding temperatures in degrees fahrenheit will be found in the column to the left temperatures in celsius (centigrade) to the right F C F C F C