The beam shown is continuous over three spans, but a beam or truss may be continuous over any number of spans. In general the ends of the beam or girder may be fixed or held at the ends _A_ and _D_, so that bending moments _M_ and _M₃_ at the same points may have value. The bending moments at the other points of support are represented by _M₁_, _M₂_, etc. The points of support may or may not be at the same elevation, but they are usually assumed to be so in engineering practice. Finally, it is ordinarily assumed that the continuous structure is straight before being loaded, and that in that condition it simply touches the points of support. Whether the preceding assumptions are made or not, a perfectly general equation can be written expressing the relation between the bending moments over each set of three consecutive points of support, as _M_, _M₁_, and _M₂_, or _M₁_, M₂, and M₃. Such an equation expresses what is called the ”Theorem of Three Moments.” It is not necessary to give the most general form of this theorem, as that which is ordinarily used embodies the simplifying assumptions already described. This simplified form of the ”Theorem of Three Moments” applied to the case of Fig. 28 will yield the following two equations: 1 ₁ _Ml₁ + 2M₁_(_l₁ + l₂_) + _M₂l₂_ + ---- ∑ _W_(_l₁² - z²_)_z_ _l₁_ 1 ₂ + ----- ∑ _W_(_l₂² - z²__)z_ = 0. (40) _l₂_ 1 ₂ _M₁l₂ + 2M₂_(_l₂ + l₃_) + _M₃l₃_ + ------ ∑ _W_(_l₂² - z²_) _l₂_ 1 ₃ + ---- ∑ _W_(_l₃² - z²_)_z_ = 0. (41) _l₃_ The figure over the sign of summation shows the span to which the summation belongs. If there is but one weight or load _W_ in each span, the sign of summation is to be omitted. In an ordinary bridge structure or beam the ends are simply supported and _M = M₃ = 0_. In any case if the number of supports be _n_, there will be _n_ - 2 equations like the preceding. If the end moments _M_ and _M₃_ are not zero, they will be determinable by the local conditions in each instance. In any event, therefore, they will be known, and there will be but _n_ - 2 unknown moments to be found by the same number of equations. When the moments are known the reactions follow from simple formulæ.