Learning Goal: To calculate internal forces in structural members under different loading and support conditions. To design a structural member, it is necessary to know the resultant forces and moments within the member to ensure the material will be able to support the loading. The method of sections is used to determine internal loadings. Consider the cantilever beam shown in the image below: (Figure 1) If the internal loadings acting on the beam at B are to be determined, we make an imaginary cut at section a-a perpendicular to the axis of the beam and separate the beam into two segments. The internal loadings at B then become external on the free-body diagram of each segment, as shown in the image below: (Figure 2) The force component NB acting perpendicular to the cut, or parallel to the axis of the beam, is called the normal force; the force component VB acting tangentially to the cut, or perpendicular to the axis of the beam, is called the shear force; the couple moment MB is called the bending moment. The forces and moments acting on the two segments act in opposite directions, as required by Newton's third law, and can be determined by applying the equilibrium equations to the free- body diagram of either segment. Provided the structural member is homogeneous and is not irreversibly deformed, these loadings can be considered to act at the centroid of the member's cross-section. The customary sign conventions are to say the normal force is positive if it creates tension, the shear force is positive if it causes the beam segment to rotate clockwise, and a bending moment is positive if it causes the Figure 1 of 4 > Part A - Internal Loading Due to a Variable, Distributed Load Consider the cantilever beam and loading shown in the image below where d = 15.0 ft, wB = 730 lb/ft, and wд 310 lb/ft. (Figure 3) == Determine the magnitudes of the internal loadings on the beam at point C. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) Nc =, Vc = Mc = Submit ΜΕ ΑΣΦ Η vec Part B - Internal Loading on a Semicircular Member ? lb, lb, lb.ft Consider the semicircular member and loading shown in the image where d = 0.570 m and F = 75.0 N. (Figure 4) Determine the magnitudes of the internal loadings on the beam at point B. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) a B P₂ NB =, VB =, MB = Submit ΜΕ ΑΣΦΑ vec ? N, N, N-m