Introduction to Structural Engineering STRUCTURE I ARCH208

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.

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

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.

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.

Frames Braced Rigid

Frames Continued Frame

Flat Plate

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.

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

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.

Planar Truss Truss C T Forces in Truss Members

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

Shells

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.

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.

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).

Arch Arch

Beam/Girder

Cable Suspended Structure

Cable Stayed Bridge

Folded Plate

Moment of a Force

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.

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

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

Direction FMD

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

A MO =

B MO =

C m N m m MO =

D m m m N MO =

E MO =

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

Resultant Moment

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”

Example3 Determine the resultant moment of the four forces.

Example4 Determine the moment of the force about A.

Example5 Determine the moment of the force about 0.

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

Equilibrium of a Rigid Body

Equilibrium of a Rigid Body

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

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.

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

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

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

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

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

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

Solution Free-Body Diagram

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

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

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

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

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

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

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

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

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

Solution

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

Solution

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

Solution

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.

Solution

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.

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.

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.