1. Introduction to Structural Engineering
STRUCTURE I
ARCH208

2. relationship between structure and architecture
a situation in which the form of a building is determined solely by the architect with the engineer being concerned only with making it stand up.
the situation in which architect and engineer collaborate fully over the form of a building and evolve the design jointly. As will be seen, the type of relationship which is adopted has a significant effect on the nature of the resulting architecture.

3. STRUCTURES How can we define a structure?
A structure is an arrangement of designed components that provides strength to a built device such as a building, bridge, dam,.
A structure must
be capable of carrying the load they were designed for without failing, and
support the load or object in the correct position.
STRUCTURES

4. Types of structures 1. MASS STRUCTURES
They can be made by, piling up or forming similar materials into a particular shape or design.
Sand castles, dams and brick walls are manufactured mass structures.
Advantages: They are hold in place by its own weight losing small parts often has little effect on the overall strength of the structure.

5. Types of structures 2. FRAME STRUCTURES
They have a skeleton of strong materials, which is then filled and covered with other materials, supporting the overall structure. Most of the inside part of the structure is empty space.
Buildings made of steel beams and colomns are an example of frame structures. Other example is when the structure is made of reinforced concrete.

6. Frames
Braced
Rigid

7. Frames Continued
Frame

8. Flat Plate

9. Types of structures 3. TRUSSES
Trusses are frame structures formed by triangles.
The triangle is the most rigid frame structure and many complex structures are based on triangles. The technique used in these type of structures is called triangulation.

10. Types of structures 3. TRUSSES
When forces are applied to a simple four-sided structure, it can be forced out of shape. A structure which behaves in this way is said to be non-rigid
By adding an extra bar the structure can no longer be forced out of shape, and is said to be rigid.
The effect is known as triangulation

11. Types of structures 3. TRUSSES
Alternatively, a frame structure can be made rigid by the use of gusset plates. A GUSSET is a piece of material used to brace and join the members in a structutre.

12. Planar Truss
Truss C T
Forces in Truss Members

14. Types of structures 4. SHELL STRUCTURES
Structures, which keep their shape and support loads, even without a frame, or solid mass material inside, are called shell structures. These structures use an outer layer of material, to provide their strength and rigidity. The shape of a shell structure spreads forces throughout the whole structure, which means every part of the structure supports only a small part of the load, giving it its strength.
Examples include: egg cartons, water containers, gas tanks and cars

15. Shells

16. Types of structures 5. SUSPENSION STRUCTURES
Suspension structures are those with horizontal planes (road decks, roofs, and even floors) supported by cables (hangers). Suspension bridges are good examples of these structures. In these bridges, cable suspended via towers hold up the road deck.

17. Types of structures 6. VAULTED STRUCTURES
Vaulted structures are those formed with arches. They are usually used to provide a big space with a ceiling or roof. The weight of the ceiling is conducted through the vault into the pillars (or columns) that are supporting it, and from those pillars into the foundation of the building.
Different shapes in the vaulted structures have been used through history and depending on the different cultures.

18. Types of structures 7. GEODESIC STRUCTURES
Geodesic structures (usuaslly called geodesic domes) are a kind of shell structures in which the shell is formed by polygons (usually triangles).

19. Arch
Arch

21. Beam/Girder

23. Cable Suspended Structure

25. Cable Stayed Bridge

27. Folded Plate

28. Moment of a Force

29. Objectives
Introduce the concept of the moment of a force and show how to calculate it in 2 dimensions.
Define the moment of a couple.
Present methods for determining the resultants force systems.

30. Force F tends to rotate the beam clockwise about A with moment
MA = FdA
Force F tends to rotate the beam counterclockwise about B with moment
MB = FdB
Hence support at A prevents
the rotation

31. Magnitude For magnitude of MO, MO = Fd
where d = moment arm or perpendicular distance from the axis at point O to its line of action of the force
Units for moment is N.m

32. Direction
FMD

33. Example1
For each case, find the moment
of the force about the point O

34. A
MO =

35. B
MO =

36. C m N m m
MO =

37. D m m m N
MO =

38. E
MO =

39. Example2 Determine the moment of the 800 N
force about points A, B, C, and D

40. Resultant Moment

41. Principles of Moments Also known as Varignon’s Theorem
“Moment of a force about a point is equal to the sum of the moments of the force’s components about the point”

42. Example3
Determine the resultant moment of the four forces.

43. Example4
Determine the moment of the force about A.

45. Example5
Determine the moment of the force about 0.

47. Important Points
The moment of a force indicates the tendency of the body to cause rotation about a point.
Magnitude M=Fd d is  distance from point O to line of action of F
3. Principle of Moments

48. Equilibrium of a Rigid Body

49. Equilibrium of a Rigid Body

50. Chapter Objectives
Develop the equations of equilibrium for a rigid body
Concept of the free-body diagram for a rigid body
Solve rigid-body equilibrium problems using the equations of equilibrium

51. If rotation is prevented, a couple moment is exerted on the body.
Free Body Diagrams
Support Reactions
If a support prevents the translation of a body in a given direction, then a force is developed on the body in that direction.
If rotation is prevented, a couple moment is exerted on the body.

55. Free Body Diagrams Cable exerts a force on the bracket
Type 1 connections
Rocker support for this bridge girder allows horizontal movements so that the bridge is free to expand and contract due to temperature
Type 5 connections

56. Free Body Diagrams
Concrete Girder rest on the ledge that is assumed to act as a smooth contacting surface
Type 6 connections
Utility building is pin supported at the top of the column
Type 8 connections

57. Free Body Diagrams
Floor beams of this building are welded together and thus form fixed connections
Type 10 connctions

58. Imagine body to be isolated or cut free from its constraints
Free Body Diagrams
Procedure for Drawing a FBD
1. Draw Outlined Shape
Imagine body to be isolated or cut free from its constraints
Draw outline shape
2. Show All Forces and Couple Moments
Identify all external forces and couple moments that act on the body

59. Free Body Diagrams
3. Identify Each Loading and Give Dimensions
Indicate dimensions for calculation of forces
Known forces and couple moments should be properly labeled with their magnitudes and directions

60. Example 1
Draw the free-body diagram of the uniform beam.

61. Solution
Free-Body Diagram

62. Support at A is a fixed wall
Solution
Free-Body Diagram
Support at A is a fixed wall
Three forces acting on the beam at A denoted as Ax, Ay, Az, drawn in an arbitrary direction
Unknown magnitudes of these vectors

63. Equations of Equilibrium
For equilibrium of a rigid body in 2D,
∑Fx = 0; ∑Fy = 0; ∑MO = 0
∑Fx and ∑Fy represent sums of x and y components of all the forces
∑MO represents the sum of the couple moments and moments of the force components

64. Equations of Equilibrium
Procedure for Analysis
Free-Body Diagram
Force or couple moment having an unknown magnitude but known line of action can be assumed
Indicate the dimensions of the body necessary for computing the moments of forces

65. Equations of Equilibrium
Procedure for Analysis
Equations of Equilibrium
Apply ∑MO = 0 about a point O
Unknowns moments of are zero about O and a direct solution the third unknown can be obtained
Orient the x and y axes along the lines that will provide the simplest resolution of the forces into their x and y components
Negative result scalar is opposite to that was assumed on the FBD

66. Example 2
Determine the horizontal and vertical components of reaction for the beam loaded. Neglect the weight of the beam in the calculations.

67. Solution 600N represented by x and y components
Free Body Diagrams
600N represented by x and y components
200N force acts on the beam at B

68. Example 4
Three loads are applied to a beam as shown. Determine the reactions at A and B when P = 70kN.
27kN P
0.9m
1.8m
0.6m

69. Solution
27kN
70kN
1.8m
0.9m
0.6m A By Bx

70. Example 5
Three loads are applied to a beam as shown. Determine the reactions at A and B.
100 N
200 N
300 N
900 mm d
300 mm

71. Solution

72. Example 6
Distributed load applied to AB beam. Determine the support reactions.
250 kn/m
6 m
4 m
6 m

73. Solution

74. Example 9
A beam supports a distributed load as shown. Determine the equivalent concentrated load and the reactions at the supports

75. Solution

76. The 400-kg uniform I beam supports the load shown
The 400-kg uniform I beam supports the load shown. Determine the reactions at the supports.

77. Solution

78. Ex :Determine the horizontal and vertical components of reaction at the pin A and the tension developed in cable BC used to support the steel frame.

80. Ex: The jib crane is supported by a pin at C and rod AB
Ex: The jib crane is supported by a pin at C and rod AB. If the load has a mass of 2000 kg with its centre of mass located at G, determine the horizontal and vertical components of reaction at the pin C and the force developed in rod AB on the crane when x = 5 m.

82. Ex: Determine the horizontal and vertical components of reaction at the pin A and the force in the cable BC. Neglect the thickness of the members.