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# Chapter 1

By Dustin Hayes,2014-09-23 10:24
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Chapter 1

Chapter 1 Introduction

Frame of members which carries the load is referred as a structure in engineering.

i.e.

? Crane’s jib;

? support frame of crane;

? support frame of civil construction.

To study the internal forces of the structure is the target of this course.

The structures in engineering are very complex, so we must simplify the structures in several aspects:

1.1 Computing Model

Real structures are usually too complex for rational analysis. They have to be reduced to simplified and idealized model prior to computation. The computing model strikes a balance between the reality of structure and the simplicity of the computation

For example:

Fig.1-1(a) Fig.1-1(b)

Fig 1-1(a) shows a concrete beam supported by walls at its two ends; a heavy weight is suspended from the beam.

If we analyses according to reality, we cannot determine the reaction forces because we don’t know how distribution of the reaction forces.

We simplify:

The following factors are taken into account:

? the width of the walls (b) is very small comparison with the length of the beam (l).

? The beam can’t move in horizontal direction because of friction between the beam and walls, but it can lengthen or shrink (age) due to change of temperature.

? the beam is represented by a line

So the Fig1-1(a) can be simplified as Fig1-1(b). Fig1-1(b) is referred to as computing model.

How to simplify is a very important problem. We can do it from three aspects as following:

1. Simplification of Members

In analysis ?we use the center-line to represent a member ignoring its lateral dimension ;( a)

? Small bending beam can be simplified by a center-line ;(b)

? Beam column which has small inclined angle can be drawn with vertical or horizontal line; (c).

(a) (b)

(c) ;

Fig.1-2

2. Simplification of Joints

When the members are connected together, the mutual displacements of the members are restrained. The connection point is called joint. There are two types of joint:

? Hinge Joint. (Small resistance in bending)

A hinge joint restrains the translation of one member relative to the others, the members can have independent free rotations about the center of the hinge. (a)

? Rigid Joint

The members from a monolithic body, they can move and translate, as a group, but can not move with respect to each other.

When the deformation of the structure was taken place, the angle included between members can’t change (invariable).

Included angle ------夹角 monolithic---- 单一！统一的

(a) (b)

Fig.1-3

3. Simplification of supports

The member that connects the structure to some stationary foundation is called support.

The functions of support are:

a. Locating structure;

b. Delivering the load of structure to foundation or base.

In such support, only the motion in a direction perpendicular to the support surface beneath the roller is restricted.

;

1-4 (a)

It permits slight rotation and movement. There is a reaction force R.

? Hinge Support

;

Fig. 1-5

This support:

Only the free rotation about the hinge A can take place. There is frictionless in the pin hole.

Two reaction forces pass through the same hinge point A.

? Fixed support

1-6(a) 1-6(b)

Fig.1-6

This support prevents motions, which both translation and rotation.

There are three reaction forces, M .it also be represented by three link supports (1-6)

? Fixed direction support (定向支座)

(a) (b)

Fig.1-7

The support permits the member’s translation in only one direction (1-7).

1.2 Classification of structures

Structures may be classified in various ways:

? in dimensions domain :

Structures can be classified into plane structure and space structure.

a. Members in a plane.

a. Members in more planes.

b. Loads in two or more planes.

If members of the structure are its loads are also in the same plane .It is called

plenary structure.

If members are not in a plane or its loads are not lie in the same plane. ? In Restraints

Statically determinate structure All reaction forces and internal forces can be determined by statically balance equations.

Statically indeterminate structure All reaction forces and internal forces can not be determined by statically balance equations.

? In Geometry

Framed Structure

A framed structure is comprised of bars, of which the dimension of the length. Thin-wall Structure

When the thickness of the structure is very small in comparison with its overall dimension.

Massive Structure

The three dimensions of magnitude.

In this course only planar-framed structures is paid attention. 1.3 planar-framed structures can be divided into the following forms: ? Beam

A beam is an elastic member which can stand transverse forces. It consists of either a single member or a system of members.

(single)

(system)

? Arch

a) Arch is composed of curved members;

b) Horizontal reaction force can be.

? Truss

A truss consists of bars which connected at their end joint. When all loads act at the joints, every member is subjected to axial force.

? Frame

A frame is consisting of straight members which hinged or rigidly connected at their ends. Frame can resist bending, shearing, tension or compression. ? Composite Structure

A composite structure is a combination of several structures described as above.

Load is meant by external active forces imposed on structures.

Load can be divided in various ways:

Duration of application:

Movable load are those which position can change:

I.e. snow, person on structure. Furniture on a house.

Moving load is meant by load can be moved by their own power.

I.e. trolley of crane

? Manner of application:

Static load: its magnitude, position and direction are not change.

Dynamic load: give rise to vibration of structure.

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