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Horizontal Shear Stresses in Beams

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This textbook on Structural Analysis is suitable for all Civil Engineering, Building Construction, Architecture, and Quantity Surveying students, in both Diploma and Degree levels of education, who wish to gain an understanding of the theory of structures. It will be especially helpful as a supplementary reading book and as standard teaching material. The worked examples included at the end of every chapter contain standard exam-type problems that will enable the learner to know how to tackle typical problems in structural analysis. The book also contains clear, well-labeled diagrams that will assist the learner in painting a mental picture in order to relate what he or she is studying to real-life examples. It is the hope, wish, and prayer of the author that this book will be instrumental in providing a sound foundation for the learner as he or she furthers their education.

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1.0 COMPOSITE MATERIALS

1.1 Introduction
Composite materials are materials that are made from at least two distinct materials that have different
physical and/or chemical properties. When these distinct materials are combined, the resultant composite
material possesses characteristics that are different from its constituent materials. Examples of composite
materials include:
(i) Reinforced concrete (concrete and steel).
(ii) Reinforced concrete and masonry.
(iii) Composite wood e.g. plywood.
(iv) Metal matrix composites.
(v) Ceramic matrix composites.
(vi) Glass fiber reinforced plastics.
(vii) Carbon fiber reinforced plastics.

, Figure 2.1: Examples of Composite Materials
1.2 Advantages of composite materials
(i) Composite materials can be lighter in weight.
(ii) Composite materials can achieve optimal strength.
(iii) Composite materials can have improved fatigue life.
(iv) Composite materials can be corrosion resistant.
(v) Composite materials can have reduced assembly costs due to fewer detail parts.

1.3 Disadvantages of composite materials
(i) Composite materials can have high raw material costs.
(ii) Composite materials can have high fabrication costs.
(iii) Composite materials can be adversely affected by temperature and moisture.
(iv) Composite materials can have high recurring maintenance costs.
(v) Composite materials can have high susceptibility to impact damage.

2.4 Analysis of bars of composite sections (Integrated)
As described in section 2.1, a bar made up of two or more bars of equal lengths but of different materials
rigidly fixed with each other and behaving as one unit for extension or compression when subjected to an
axial tensile or compressive load, is called a composite bar. For a composite bar, the following two points
are important.

Compatibility: The extension or compression in each bar is equal, hence deformation per unit
length i.e. strain in each bar is equal.

Equilibrium: The total external load on the composite bar is equal to the sum of the loads
carried by each different material.




Figure 2.2


Figure 2.2 (a) shows a composite bar, made up of two different materials, 1 and 2, and subjected to
tension as shown in Figure 2.2 (b). Let:

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