Direct Stress and Strain Tutorial Questions
Pin jointed frames, generally, transfer the applied loads by inducing axial tensile or compressive forces in the individual members. The magnitude and sense of these forces can be determined by using standard methods of analysis.
The following tutorial questions require that the forces in the individual elements be solved by either the "method of sections" or the "method of joints".
The "method of sections" involves the application of the three equations of static equilibrium to a two dimensional plane frame. An imaginary section line cuts the frame in two. Since there are only three equations of equilibrium, the section through the frame must not include any more than three members for which the internal forces are unknown.
The "method of joints" considers the isolation of each individual joint. For each joint, as the forces are coincident the moment equation is of no value leaving only two equations of equilibrium available to resolve the forces in the members. The equilibrium of each joint must be considered in a sequence that ensures that there are no more than two unknown member forces in each joint under consideration.
- The analysis associated with these tutorial questions will round all your input values as follows:
- Forces, e.g. vertical and horizontal reactions (kN) - 1 decimal place.
- Dimensions (m) - 3 decimal places.
- Angles (°) - 1 decimal place.
- Numeric answers are required in all the fields. If you calculate a force as being zero, enter zero (0) in the appropriate field.
- You are only able to print the current question as a tutorial question if you have not submitted your answers.
- Once a tutorial question has been printed, you will not be able to submit your answers, or see the solution to that particular question.
- ∅ - Diameter of an object (mm).
- σ - Compressive or tensile stress within a material (N/mm²): σT - tensile stress, σC compressive stress.
- ε - Strain, used to measure the deformation or extension of a body that is subjected to a force or set of forces.
- δ - Displacement of a point of an object to an alternate position (mm).
- Δ - Change in length, area or thickness of an object (mm).
- E - Young's Modulus: property that measures stiffness; it defines a relationship between stress and strain (N/mm²).
- ν - Poisson's ratio: the proportional decrease in a lateral measurement to the proportional increase in length.
- C/C - The distance between the centres of objects (mm).