Deflection of beams can be a tricky and difficult for most undergraduate mechanical engineering students as it involves some intituitive understanding on the topic of deflection as well as on the topic of shearing force and bending moment diagrams. Check out the questions below, which will help you explore your level of competency in the topic of deflection of beams.
Q1) Calculate the maximum deflection of a uniformly loaded simple beam as shown in the figure if the span length L = 2 m, the intensity of the uniform load q = 2 kN/m, and the maximum bending stress, . The cross section of the beam is square and the material is aluminum having modulus of elasticity E = 70 GPa.
Q2) Derive the equations of the deflection curve for a simple beam AB loaded by a couple acting at a distance 'a' from the left hand support, as shown in the figure. Also, determine the deflections at the point where the load is applied.
Q3) A simple beam with a uniform load is pin supported at one end and spring supported at the other. The spring has a stiffness of . Derive the equation of the deflection curve by starting with the third order differential equation (the shear-force equation). Also, determine the angle of rotation at support A.
Q4) A beam ABCD consisting of a simple span BD and an overhang AB is loaded by a force P acting at the end of the bracket CEF, as shown the figure.
- Determine the deflection at the end of the overhang.
- Under what conditions is this deflection upward? Under what conditions it is downward?
Q5) A beam ABC having flexural rigidity EI = 75 kN.m2 is loaded by a force P = 800 N at end C and tied down at end A by a wire having axial rigidity EA = 900 kN. What is the deflection at point C when the load is applied?
Q6) Find the horizontal deflection and vertical deflection at the free end C of the frame ABC shown in the figure. (The flexural rigidity EI is constant throughout the frame.)
Q7) The frame shown in the figure consists of a beam ACB supported by a strut CD. The beam has length 2L and is continuous through joint C. A concentrated load P acts at the free end B. Determine the vertical deflection at point B due to the load.