1. Strength of Materials
Most steel item used in ship building are divided into 4 general categories.
Beams
Plates
Columns
shafts

2. Strength of Materials
Each of the 4 groups have their individual function, but also must support the other 3 groups
The coordinated functions of all groups result in a vessel hull forming a long square beam or girder
Strength for the hull girder is determined by calculation based on a Trochoidal Wave

3. Strength of Materials Trochoidal Wave
Wave length from crest to crest is equal to the length of the vessel
Wave height is equal to 1/20th of the length of the vessel
The use of a wave of this size will determine the maximum load on the hull girder, and scantlings required for construction

4. Strength of Materials

5. Strength of Materials

6. Strength of Materials Structural Terminology:
Load- The total force acting on a structure, usually expressed in pounds or tons
Stress- The force per unit area, usually expressed in pounds or tons per square inch
Strain- The distortion resulting from stress

7. Strength of Materials
Tensile Stress- Occurs between 2 parts of a body when each draws the other toward itself
Ex. A tie rod subjected to a steady pull
Formula:
Ts=Pull = P
Area A

8. Strength of Materials
Compressive Stress- This is just the reverse of Tensile Stress
Ex. A tie rod subjected to a steady push
The same formula applies

9. Strength of Materials
Shearing Stress- The tendency of one body to slide over another part is known as shear
The magnitude of this tendency to slide at any point is termed Shearing Stress
Formula:
Ss= Pull = P
Area of the rivet A

10. Strength of Materials

11. Strength of Materials
Ultimate tensile strength of mild steel (primary steel used in ship construction) is 28 to 32 tons per square inch
Ultimate shearing Strength of mild steel is 22 tons per square inch
Steel flattens when compressed at about 18 tons per square inch

12. Strength of Materials

13. Strength of Materials Diagram explanation:
Working Range: linear line between the 0 point and point “A”

14. Strength of Materials
Point “A” is also refered to as the “Limit of Elasticity”
The point at which metal will no longer return to its original shape

15. Strength of Materials

16. Strength of Materials
If the material is loaded (even slightly) beyond point “A”, it will yield at point “B”, the “Yield Point”.
A further slight increase in load will cause the metal to stretch uniformly until it reaches point “C”, the “Yield Overcome”.

17. Strength of Materials

18. Strength of Materials
At point “C”, the metal becomes harder, so the yield is overcome.
If a slight additional weight is then added, the metal will stretch out of all proportion to the load applied until it reaches point “D”, the “Ultimate Strength”.
The metal will fail at point “E”

19. Strength of Materials

20. Strength of Materials
Curves such as the one illustrated for mild steel are available for most metals used in ship construction
The generation of these curves is known as “Testing to Destruction” as the sample must be destroyed to determine the failure point

21. Strength of Materials Safety Factors
Factors of safety (F.S.) are build into ships to allow for exceptional loads not considered by the standard trochoidal wave model. Vessel may be subjected to extreme weather conditions or, due to corrosion and wastage, the original hull steel may be weakened. The standard F.S. is considered 4.

22. Strength of Materials
Safety Factors are based on the Ultimate Strength of the sample, or point “D”. As the working range is about ½ of that, the actual, practical factor of safety is only 2.

23. Strength of Materials
When referring to ships, there are 2 very broad phases of strength:
Local Strength
Hull-girder Strength

24. Strength of Materials Local Strength
The strength of individual parts of a ship
Hull-girder Strength
The strength of the ship as a whole

25. Strength of Materials Class Societies
Class societies are the regulator that actually determine the scantlings of such construction components as beams, stiffeners and shell plating. Most are insurance driven and are based on catastrophic loss in the past.

26. Strength of Materials Bending Moment-
A moment of a force about any line is the product of the force times the perpendicular distance to that line.

27. Strength of Materials

28. Strength of Materials Example A
100 lbs is located 4’ from the end of a board imbedded in a wall
B.M. = Weight x Distance
B.M. = 100lbs x 4’
B.M. = 400 ft-lbs

29. Strength of Materials

30. Strength of Materials Example B
100 lbs is located 8’ from the end of a board imbedded in a wall
B.M. = Weight x Distance
B.M. = 100lbs x 8’
B.M. = 800 ft-lbs

31. Strength of Materials

32. Strength of Materials Example C
200 lbs is located 4’ from the end of a board imbedded in a wall
B.M. = Weight x Distance
B.M. = 200lbs x 4’
B.M. = 800 ft-lbs

33. Strength of Materials Beams-
Horizontal strength members loaded vertically
The beam in the next slide is a homogeneous material and rectangular, it is symmetrical
The ends of the beam are considered free as they are not imbedded in the wall

34. Strength of Materials

35. Strength of Materials
A load applied to the center of the beam will cause a deflection. The upper surface will shorten, the lower surface will lengthen, and the middle will remain neutral.
The upper surface must be under compression.
The lower surface must be under tension

36. Strength of Materials
As compression and tension are opposite forces, there must be a layer in the beam where the forces are neutral.
The zero point is located along the center of gravity (centroid) of the beam.

37. Strength of Materials

38. Strength of Materials
If a beam of similar size is made up of 5 individual layers that are free to slip over one another, the top 2 layers would not be under compression as they are allowed to slip, the bottom 2 layers are not under tension. The middle will not be neutral.
This beam will carry only 1/5th the load of a solid or laminated beam.

39. Strength of Materials

40. Strength of Materials
The depth of a solid beam controls its resistance or strength. Another way of considering this is the farther from the neutral axis the compression and tension edges are, the stronger the beam.

41. Strength of Materials Example: Formula: Relative Strength=(D2/D1)2
where D1 is the depth of the smaller of the 2 beams considered.
Using a 2” x 4” and a 2” x 8” we can see
(8/4)2= 4 or the 2” x 8” beam is 4 times stronger than the 2” x 4” beam

42. Strength of Materials
In the beam with 5 individual members, each 1” thick, compared to a similar sized solid beam 5” thick, the same formula applies
(D2/D1)2=Relative Strength
(1”/5”)2= 1/25th as strong for each piece
The five pieces considered together will be 1/5 as strong

43. Strength of Materials
Because the maximum force (compression and tension) on a beam is concentrated at the upper and lower edge, the material of the rectangular beam can be re-distributed to the upper and lower edges, it will gain a great deal of strength without gaining weight,

44. Strength of Materials

45. Strength of Materials
There are 5 factors that determine the size of a beam:
1) Type and amount of load on the beam
2) Distance between supports
3) Type and efficiency of end connections
4) Number of supports
5) The material the beam is constructed of.

46. Strength of Materials Type and amount of load on a beam
A) Concentrated load
B.M.= WL/4
W= weight
L= distance between supports
Example: 2 tons x 10 ft/ 4 = 5 ft-tons

47. Strength of Materials

48. Strength of Materials Type and amount of load on a beam
B) Uniform loan
B.M.= WL/8
W= weight
L= distance between supports
Example: 2 tons x 10 ft/8 = 2.5 ft-tons

49. Strength of Materials

50. Strength of Materials
Distance between supports ( often referred to as span)
A) Deflection of a rectangular free-end beam varies as the cube of the span
Example: A 10’ span has a deflection of 1”
What will be the deflection on a beam with a 20’ span?
(S2/S1)3= (20’/10’)3= 8 inches

51. Strength of Materials

52. Strength of Materials Distance between supports
B) Strength of a rectangular free-end beam varies inversely as the span
Example: A 10’ span will support 10 tons
How much weight will a 20’ span support?
Relative strength= span A/span B
10’/20’=.5
10 tons x .5 = 5 tons

53. Strength of Materials Type and efficiency of end connections
A) A fixed-ended rectangular beam will support twice as much concentrated load as a free-ended beam
B) The deflection of a fixed-ended rectangular beam is 1/4th that of a free-ended beam

54. Strength of Materials

55. Strength of Materials Effects of number of supports
The greater the number of supports in a given distance, the shorter the span. A shorter span means a smaller bending moment

56. Strength of Materials Material the beam is constructed of
Most ship construction is mild-steel.
Other materials used include:
Stainless Steel
High tensile steel
Aluminum

57. Strength of Material Columns
A strut placed such that it is loaded vertically (also referred to as a stanchion or pillar)
Columns are usually symmetrical (round)

58. Strength of Materials Shafts
A shaft subjected to a twisting moment is said to be in torsion
The twisting moment is referred to as torque
Torque (lb-ft)= horsepower x 5252/RPM
The higher the RPM, the less torque

59. Strength of Materials Example:
A 5,000 horsepower 80 RPM engine will require about the same size shaft as a 20,000 horsepower 320 RPM engine
Torque= 5,000 x 5252/80= lb-ft
Torque= 20,000 x 5252/320= lb-ft

60. Strength of Material Continuity of strength
Vessels must be constructed such that stresses may be gradually and continuously dissipated.
No part should be oversized or undersized
A discontinuity or change in shape will cause a concentration of stresses and may result in a failure

61. Strength of Materials

62. Strength of Materials

63. Strength of Materials