190 likes | 353 Views
Mechanics of Materials Lab. Lecture 5-6 Beam Mechanics of Materials Laboratory Sec. 3-4 Jiangyu Li University of Washington. Inclined Load. Notice the sign convention: positive Mz compress upper part , negative stress; positive My extend front part , positive stress!. Inclined Load.
E N D
Mechanics of Materials Lab Lecture 5-6 Beam Mechanics of Materials Laboratory Sec. 3-4 Jiangyu Li University of Washington
Inclined Load Notice the sign convention: positive Mz compress upper part, negative stress; positive My extend front part, positive stress!
Inclined Load Stress Neutral axis
Asymmetrical Beam The origin of y and z axes must be placed at centroid C; orientation is arbitrary.
Sign Convention for Curvature Similar equation apply to Bending toward z axis Note difference with sign convention in bending moment
Asymmetric Beam When z axis is the neutral axis; If z is a principal axis, My=0, bending in x-y plane, analogous to a symmetric beam
Asymmetric Beam When y axis is the neutral axis; If y is a principal axis, Mz=0, bending in x-z plane, analogous to a symmetric beam
Asymmetric Beam • When an asymmetric beam is in a pure bending, the plane in which the bending moments acts is perpendicular to the neutral surface only if the y and z axes are principle centroidal axes and the bending moment acts in one of the two principle plane. In such case, the principle plane in which bending moment acts becomes the plane of bending and the usual bending theory is valid
Analysis of Asymmetric Beam • Locating the centroid, and constructing a set of principal axes • Resolving bending moment into My and Mz • Superposition
Analysis of Asymmetric Beam A channel section C 10x15.3 c=0.634 Iy=2.28 in4, Iz=67.4 in4 yA=5.00 in, zA=-2.6+0.634=-1.966 in Calculating bending stress Locating neutral axis
Curved Beams Positive M Neutral axis is no longer the centroidal axis
Curved Beams Recover to straight beam Curvature is large, e is small, rn is cloase to rc
Curved Beam Pay attention to the sign of s
Curved Beam Pay attention to the sign of s
Assignment • Read Mechanics of Materials Lab Sec. 4 • 4.26(e), 4.72 posted online