I am a 3rd year civil engineering student and this is the first time i come across this problem and i am struggling with it. My problem here is that i don't know how to draw a shear force and bending moment diagram for a trapezoidal load on a beam with fixed supports at both ends. I know how to find the support reactions but i need an equation to find the maximum bending moment at mid-span. Are there any standard equations to determine the different points on the Bending moment digram for trapezoidal loading or do i have to divide my beam into 3 section (1. left triangular loading, 2. UDL, 3. right triangular loading ) and then superimpose the resulting diagrams for the 3 sections. I really need some help here.....i have searched for hours online and i couldn't find anything for this.