(BQ) Part 2 book "Applied strength of materials for engineering" has contents: Stresses in beams, beam deflection, combined stresses, statically indeterminate beams, visualizing stress and strain, buckling of columns. | Chapter 9: Stresses in Beams Chapter 9: Stresses in Beams P In the last chapter, we learned how to draw shear and bending moment diagrams for beams. These diagrams tell us the location and magnitude of the maximum shear load and maximum bending moment. We can use Vmax and Mmax to calculate the maximum shear stress and max. bending stress in a beam, then we can compare these results with the allowable shear stress and bending stress of the material. If the actual value is less than the allowable value, then the beam is safe; if the actual value is greater than the allowable, then we need to select a different beam. A RA Load diagram B L/2 L/2 RB Deflection diagram Δ Δmax Vmax Bending Stress in Beams A point load at the midspan of a beam makes the beam bend. We can sketch a deflection diagram to show this bending. The deflection diagram shows the beam as if it had no depth, because it is easier to draw a curve than to draw a double curve with shading. A real beam has depth, and when it is bent, the top surface shortens while the bottom surface top surface has a negative strain, while the bottom surface has a positive strain. Plot strain vs. depth: the strain varies linearly from top to bottom, and is zero at the centroidal axis. We saw in Chapter 2 that materials like steel and aluminum follow Hooke's law: the ratio of stress/strain is Young's modulus, a constant. Therefore, the stress in –εmax the beam also varies linearly from top to bottom, and is zero at the centroidal axis of the beam. We call this axis the neutral axis, where stress is This bending stress acts perpendicular to the cross-sectional area of the beam, so the stress is a normal stress; it is negative on the top and positive on the bottom. V Vmax Mmax Shear diagram Moment diagram M Side views of the beam –σmax neutral axis +σmax +εmax We can calculate the bending stress at any position y from the neutral axis: the stress is proportional to the distance from .
