The state of stress at a point is completely determined when: 1. the stress vectors on three different planes are specified 2. the stress vectors on two different planes are speciale 3. the stress vectors one arbitrary plane is spec-

A Cauchy stress component at a given(fixed) point P of a structure in equilibrium under the action of external loads is defined when 1. the direction of the face on which the stress component acts is specified 2 the direction of the force from which the stress component is derived is specified None of the above statements

We are going to consider the forces exerted on a material. These can be external or internal. External forces come in two flavors: body forces(given per unit mass or volume) and surface forces(given per unit area). If we cut a body of material in equilibrium under a set of external forces along a plane as shown in fig. 1. and consider one side of it we draw two conclusions: 1 the equilibrium provided by the loads from the side taken out is provided by a set of forces that are distributed among the material particles adjacent to

Before we look specifically at thin-walled sections, let us consider the general case (i.e, thick-Walled) Hollow thick-walled sections Figure 12.1 Representation of a general thick-walled cross-section 中=c2 on one boundary φ=c1 on one boundary This has more than one boundary(multiply-connected do=0 on each boundary

We will start by studying the motion of a particle. We think of particle as a body which has mass, but has negligible dimensions. Treating bodies as particles is, of course, an idealization which involves an approximation. This approximation may be perfectly acceptable in some situations and not adequate in some other cases. For instance, if we want to study the motion of planets it is common to consider each planet as a particle

is a vector equation that relates the magnitude and direction of the force vector, to the magnitude and direction of the acceleration vector. In the previous lecture we derived expressions for the acceleration vector expressed in cartesian coordinates. This expressions can now be used in Newton's second law, to produce the equations of motion expressed in cartesian coordinates

In this lecture we will look at some other common systems of coordinates. We will present polar coordinates in two dimensions and cylindrical and spherical coordinates in three dimensions. We shall see that these systems are particularly useful for certain classes of problems Like in the case of intrinsic coordinates presented in the previous lecture, the reference frame changes from point to point. However, for the coordinate systems to be presented below, the reference frame depends only on the position of the particle. This is in contrast with the intrinsic coordinates, where the reference frame is a function of the position, as well as the path

In this lecture we will look at some applications of Newton's second law, expressed in the different coordinate systems that were introduced in lectures D3-D5. Recall that Newton's second law F=ma, (1) is a vector equation which is valid for inertial observers. In general, we will be interested in determining the motion of a particle given

We have seen that the work done by a force F on a particle is given by dw =. dr. If the work done by F, when the particle moves from any position TI to any position T2, can be expressed as, W12=fdr=-(V(r2)-V(1)=V-v2, (1) then we say that the force is conservative. In the above expression, the scalar

In this lecture we will consider the equations that result from integrating Newtons second law, F=ma, in time. This will lead to the principle of linear impulse and momentum. This principle is very useful when solving problems in which we are interested in determining the global effect of a force acting on a particle over a time interval Linear momentum We consider the curvilinear motion of a particle of mass, m, under the influence of a force F. Assuming that