08-02-2013, 09:56 AM
Lecture Notes Strength of Materials
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Stress
By setting up the equilibrium conditions, the inner forces of a member subjected to an
external load situation can be determined. So far neither the material nor the type of
cross section applied for the member are being taken into account. But both material
and type of cross section obviously have an impact on the behaviour of the member
subjected to load.
To design the member therefore a closer look on how the internal forces act along its
cross section needs to be taken.
Normal Stress – Axial Loading
Within this part of the chapter the internal forces are limited to only axial forces
(normal forces) acting along the centroidal axis of a member.
Average Shearing Stress – Transverse Loading
So far the discussion focussed on normal stress, oriented perpendicular to the cutting
plane or in direction of the main axis of the member.
Stress can also act in the cutting plane thus perpendicular to the main axis of the
member. This occurs if the member is subjected to a situation of transverse loads (fig.
1.21).
Stress Analysis and Concept of Design
Every material has its individual properties. It can be ductile, flexible or brittle. It
deforms under the influence of a temperature change. It may plastically deform at a
certain stress (load) and break at another. Its properties according to perpendicular
directions may be equal (isotropic) or different (orthotropic).
To ensure a safe design, these specific material properties have to be taken into
account. The essential information is collected by conducting different tests in a
material testing laboratory.
At the failure of the material its ultimate stress is reached. The point of plastic
deformation of the material is indicated as the yield point, corresponding to the yield
stress. Taking this into account, an allowable stress can be defined for each
individual material to be used within the design analysis. These stresses such as
further indications concerning the maximum allowable deformation (serviceability of a
structure) can be found in the respective national codes.
Transformation of Stress – Oblique Plane under Axial Loading
Normal and shearing stresses, thus stress acting perpendicular and parallel to the
axis of symmetry of the member have been analysed in the previous parts of this
chapter.
The plane of cut being used to isolate a part of the member was perpendicularly
oriented in all the situations regarded so far. How about the situation of stress on an
oblique plane of cut?
Fig. 1.41 shows a member subjected to an axial load. A part of the member is
isolated by a plane of cut, inclined by the angle φ towards the axis of the member.
Setting up the free body diagram and the conditions of equilibrium the stress
components acting normal to or within the plane of cut are determined.