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The structure is statically determinate. Therefore, all influence lines will be straight lines. Parts (b) and (c) of the figure shows the influence lines for the reactions in the y-direction. Releasing the vertical reaction for A allows the beam to rotate to Δ. Likewise for part (c). Δ is typically taken as positive upwards.
R. C. Hibbeler states, in his book Structural Analysis, “All statically determinate beams will have influence lines that consist of straight line segments.” [5] Therefore, it is possible to minimize the number of computations by recognizing the points that will cause a change in the slope of the influence line and only calculating the ...
Descriptively, a statically determinate structure can be defined as a structure where, if it is possible to find internal actions in equilibrium with external loads, those internal actions are unique. The structure has no possible states of self-stress, i.e. internal forces in equilibrium with zero external loads are not possible.
A statically indeterminate structure has more unknowns than equilibrium considerations can supply equations for (see simultaneous equations). Such a system can be solved using consideration of equations of compatibility between geometry and deflections in addition to equilibrium equations, or by using virtual work .
A statically determinate beam, bending (sagging) under a uniformly distributed load. A beam is a structural element that primarily resists loads applied laterally across the beam's axis (an element designed to carry a load pushing parallel to its axis would be a strut or column).
When =, the truss is said to be statically determinate, because the (m+3) internal member forces and support reactions can then be completely determined by 2j equilibrium equations, once we know the external loads and the geometry of the truss. Given a certain number of joints, this is the minimum number of members, in the sense that if any ...
A statically determinate simply supported beam, ... Beams and columns are called line elements and are often represented by simple lines in structural modeling.
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...