Question

In the slope deflection equations, the deformations generated are due to:
i. axial force
ii. shear force
iii. bending moment

• A. only (i) and (ii)
• B. only (iii)
• C. only (i)
• D. only (i) and (iii)

Hint:

In the slope deflection method, remember that the bending moments are responsible for the rotations (angular deformations), while axial and shear forces mainly influence internal forces and displacements, not the rotations at the joints.

Answer 1

The Correct Option is B

The slope deflection equations are a set of equations used to analyze the deformation of structures like beams and frames under applied loads. These equations relate the rotations and displacements of the ends of the beam or frame to the applied loads, including moments, forces, and the stiffness properties of the structure. The key principle behind the slope deflection method is that deformations in a structure are primarily caused by bending moments, and to a lesser extent, axial and shear forces. 
1. Bending Moment: The slope deflection method primarily accounts for the deformation due to bending moments. These moments cause the beam or frame to rotate at the joints. The angle of rotation (or slope) at a joint is proportional to the applied bending moment and the beam's stiffness. In the slope deflection equations, the bending moment at a joint is a function of the slope at the joint, the stiffness of the beam, and the external loads. Therefore, bending moments are the primary cause of deformation in the slope deflection method, making option (iii) the correct choice. 
2. Axial Force: Axial forces, such as tension or compression, can cause elongation or shortening of the beam, but they do not directly affect the rotation at the ends of the beam in the slope deflection method. Axial forces can influence the internal forces and the overall stability of a structure, but they do not contribute to the angular deformation or bending that the slope deflection equations primarily focus on. Hence, axial force does not directly appear in the slope deflection equations for the purposes of calculating rotation or slope. 
3. Shear Force: Similarly, shear forces can cause deformation in the structure, but their effect is typically more localized and affects the internal shear distribution along the beam. In the slope deflection method, shear forces do not directly contribute to the rotation at the joints of the beam. Shear forces affect deflections but are not part of the slope deflection equations used to model the rotations. 
Thus, the correct answer is only (iii), as the deformations in the slope deflection method are due to the bending moment.