Beer uses a specific sign convention (positive shear rotates beam clockwise on left face). Many free PDFs ignore this and just give magnitudes. The "better" solution: Look for a PDF that explicitly shows the sign convention on each diagram. If it doesn’t, add it yourself—then your PDF becomes customized.
Composite sections in Chapter 6 (Shearing Stresses in Beams) require careful centroid calculations. The "better" solution: A superior PDF breaks the composite shape into rectangles, shows each I = I_bar + Ad^2 term, and sums them clearly. No skipping. beer mechanics of materials 8th edition solutions pdf better