INTERNAL FORCESIN BENDING 4). Planar bending: After deformation the curved axis of the beam is still in the same plane with the external forces Symmetric bending as shown in the following figure )-a special example of the planar bending q P M The plane of symmetry
11 4).Planar bending：After deformation the curved axis of the beam is still in the same plane with the external forces. Symmetric bending（as shown in the following figure）— a special example of the planar bending. The plane of symmetry M P1 P2 q
意曲向为 4.平面弯曲:杆发生弯曲变形后,轴线仍然和外力在同 平面内。 对称弯曲(如下图)平面弯曲的特例。 q P M 纵向对称面 12
12 4. 平面弯曲：杆发生弯曲变形后，轴线仍然和外力在同一 平面内。 对称弯曲（如下图）—— 平面弯曲的特例。 M 纵向对称面 P1 P2 q
INTERNAL FORCESIN BENDING M M Unsymmetrical bending if a beam does not possess any plane of symmetry, or the external forces do not act in a plane of symmetry of the beam with symmetric planes, this kind of bending is called unsymmetrical bending. In later chapters we will mainly discuss the bending stresses and deformations of the beam under symmetric bending 13
13 Unsymmetrical bending— if a beam does not possess any plane of symmetry, or the external forces do not act in a plane of symmetry of the beam with symmetric planes, this kind of bending is called unsymmetrical bending. In later chapters we will mainly discuss the bending stresses and deformations of the beam under symmetric bending
意曲内为 M M 非对称弯曲若梁不具有纵对称面,或者,梁虽具有纵 对称面但外力并不作用在对称面内,这种 弯曲则统称为非对称弯曲。 下面几章中,将以对称弯曲为主,讨论梁的应力和变 形计算
14 非对称弯曲—— 若梁不具有纵对称面，或者，梁虽具有纵 对称面但外力并不作用在对称面内，这种 弯曲则统称为非对称弯曲。 下面几章中，将以对称弯曲为主，讨论梁的应力和变 形计算
INTERNAL FORCESIN BENDING 2 Calculation sketch of the beam In general supports and external forces of the beam are very complex We should do some necessary simplification for them for our convenient calculation and obtain the calculation sketch 1). Simplification of the beams In general case we take the place of the beam by its axis Simplification of the loads The loads(including the reaction) acting on the beam may be reduced into three types: concentrated force concentrated force couple and distributed force 3). Simplification of the supports 15
15 2、Calculation sketch of the beam In general supports and external forces of the beam are very complex. We should do some necessary simplification for them for our convenient calculation and obtain the calculation sketch. 1). Simplification of the beams In general case we take the place of the beam by its axis. 2). Simplification of the loads The loads (including the reaction) acting on the beam may be reduced into three types：concentrated force、concentrated force couple and distributed force. 3). Simplification of the supports