Please explain what does it mean the Integratew dz dz Thank

Please explain what does it mean the Integrate(w dz dz)

Thank you

where Fo is the shearing force at z = 0\' Then o wdz (7.22) Furthermore, from equation (7.6), the bending moment a distance z from B is (7.23) where we have M, - 0, and so z - 0. However, as the beam is simply-supported at z 0, M, is the bending moment at wdz dz o Jo The end z L is also simply-supported, so for this end M - 0; then

Solution

Integrate(w.dz.dz) means that you are integrating the load inensity two times, and that gives you the banding moment. This method is known as graphical method. There is double integral for a reason.

When you integrate the load intesity over a range of z once, you get shear force. This is the way of finding the area under the load diagram, which equals shear force.

When you integrate it once more, that gives us the moment of the force, because this time you are finding the area under the shear force diagram, and as per graphical method this gives us the Bending Moment.

Please note that w is the load intensity with units such as N/m, kN/m or Lbs/ft etc. It is not a concentrated load , but a uniformly distributed load. So when you integrate it once, we get shear force in the units of force such as N, kN, or lbs. When you again integrate it once more w.r.t. the distance z along beam, we get moment with the units of N.m, kN.m, Lbs-ft. etc.