__________________________________________________________________________________ COURSE MODULE MODULE NO : : : DCEB 2 FT STRUCTURAL ANALYSIS BE8202
TOPIC 1 : STATICALLY DETERMINATE STRUCTURES _________________________________________________________________________ Keywords: Beam, Truss, Rigid Frames, Equilibrium, Determinate, Stable, Shear Force, Axial Force, Bending Moment, Free Body Diagram, Axial Force Diagram, Shear Force Diagram.
Objectives: Students should be able to • Understand the principle of equilibrium of forces as applies to determinate structures • Construct the free-body diagram for determinate beams, trusses and rigid frames • Draw the bending moment, shear force and axial force diagrams.
Reference Books: 1. 2. 3. R. C. Hibbeler. Structural Analysis. Prentice Hall. M S Williams & J D Todd. Structures, theory and analysis. M. S. Williams Yuan – Yu Hsieh. Elementary Theory of Structures. Prentice Hall.
Statically Determinate Structures
__________________________________________________________________________________ 1.1 INTRODUCTION The word structure describes much of what is seen in nature. Living plants, from the frailest of ferns to the most rugged of trees, possess a structural form consistent with their needs. Insects and animals play a more active role in building the structures that they need, e.g. the delicate web of the spider, etc. Humans, too, are builders of structures; but more than that, they are conceivers and designers. When the structures of humans began to reflect their ability to conceive and design them as well as to construct them, structural engineering was born, and it has grown in sophistication as it has endeavoured to meet the demands of humanity.
Determinate Beams A beam is defined as a structural member predominantly subjected to bending moment. In this chapter, only beams of symmetrical section, the centroidal axis of such beams being a straight line will be discussed. Furthermore, the beam is acted on by only transverse loading and moment loading and that all the loads and reactions lie in the plane of symmetry. For these, it follows that such a beam will be subjected to bending and shear in the plane of loading without axial stretching and twisting. Statically determinate beams may be classified as :  Simple beam : A beam that is supported at its two ends with a hinged and a roller Fig(1.1a) or their equivalents Fig(1.1b), is termed a simply supported beam or simple beam.  Cantilever beam : Fig(1.1c) shows a cantilever beam, which is fixed or built-in at one end and free at the other end. Another form of cantilever is shown in Fig(1.1d), in which the three elements of reaction of fixed support are provided by a hinge and roller closely placed at one end segment.  Simple beam with overhang : A beam may be simply supported at two points and have its end portion( or portions) extend beyond the support, as in Figs(1.1e) or (1.1f); it is then called a simple beam with overhang.  Compound beam : The beams indicated above may be connected by internal hinges or rollers to form a compound beam, such as those Figs(1.1g) and (1.1h). Care must be used in providing the connections so that instability is not produced.
Statically Determinate Structures
Fig(1.1) 1.3 Sign conventions The sign conventions for beam shear and moments are as follows:  Shear is considered positive at a section when it tends to rotate the portion of the beam in the clockwise direction about an axis through a point inside the free body and normal to the plane of loading; otherwise, it is negative [see Fig(1.2a)].  Bending moment is considered positive at a section when it tends to bend the member concave downward; other wise, it is negative [see Fig(1.2b)].