Problem 624
For the beam loaded as shown in Fig. P-624, compute the moment of area of the M diagrams between the reactions about both the left and the right reaction.
Another method of determining the slopes and deflections in beams is the area-moment method, which involves the area of the moment diagram.
The moment-area method of finding the deflection of a beam will demand the accurate computation of the area of a moment diagram, as well as the moment of such area about any axis. To pave its way, this section will deal on how to draw moment diagram by parts and to calculate the moment of such diagrams about a specified axis.
1. $\displaystyle \int du = u + C$
2. $\displaystyle \int a \, du = a\int du$
3. $\displaystyle \int (du + dv + ... + dz) = \int du + \int dv + ... + \int dz$
4. $\displaystyle \int f (x)\,dx = F(x) + C$
5. $\displaystyle \int_a^b f(x) \, dx = F(b) - F(a)$
6. $\displaystyle \int_a^b f(x) \, dx = -\int_b^a f(x) \, dx$
7. $\displaystyle \int_a^b f(x) \, dx = \int_a^c f(x) \, dx + \int_c^b f(x) \, dx$
8. $\displaystyle \int_a^b f(x) \, dx = \int_a^b f(z) \, dz$
