Calculate hollow rectangular beam deflection and bending stress.
Reading Assignment Text: Sect 6.4 through 6.7 and 6.9 ACI 318: Chap 9. Calculation of Deflection of R/C beams Review of theory of deflection of homogeneous beams in elastic flexure: x y y(x) dx w(x) It is possible to make the following observations from geometry Deflection = y(x) Slope = dy/dx Curvature = d2y/dx2 = φ=1/ρ y = φdx dx … When calculating deflection, you need to know the properties of the guide or actuator and the conditions of the applied load. Distance 'x' of the section is measured from origin taken at support A. There is a range of beam deflection equations that can be used to calculate a basic value for deflection in different types of beams . CIVL 4135 Deflection CHAPTER 13. Material and design considerations. The deflection at the free end is 3 mm downwards. The above expression can now be used to calculate the deflection at any point on the beam. Many structures can be approximated as a straight beam or as a collection of straight beams. Example: Given that a silver hollow beam of length 10 inches, width 25 inches, height 30 inches having a wall thickness of 10 inches and beam weight of 150 pounds. View the report produced for this example
into equation (6) above.
DEFLECTION 13.1. Deflection; max = 24.8 mm; min = 0 mm Maximum reaction at support A; R A_max = 53.9 kN; R A_min = 53.9 kN Unfactored dead load reaction at support A; R A_Dead = 29.3 kN The use of L/d method ‘will be adequate for avoiding deflection problems in normal circumstances’ The rigorous method of assessing deflection. The modulus of elasticity is 205 GPa. Downward deflection is negative whereas upward deflection is taken as positive. Hence, a 5m span beam can deflect as much as 20mm without adverse effect. Calculation Example – Determine the shear force and moment. This section covers shear force and bending moment in beams, shear and moment diagrams, stresses in beams, and a table of common beam deflection formulas. In practice it is the maximum deflection that is of interest and common sense would say that for this example this occurs at mid-span and can be calculated by substituting . Example - Beam with Uniform Load, Metric Units A UB 305 x 127 x 42 beam with length 5000 mm carries a uniform load of 6 N/mm. maximum deflection is limited to the beam’s span length divided by 250. The examples are quite varied, but most are not interrelated with follow-up examples in which the same problem is attacked using different methods.
Castigliano Theorem. Calculation Example – Internal forces. x=L/2=2.5m . A cantilever beam is 5 m long and has a point load of 50 kN at the free end. 13.2. Calculation Example - Calculate the deflection. Deflection of a beam (beam deflection) is calculated based on a variety of factors, including materials, the moment of inertia of a section, the force applied and the distance from support.
The above expression can now be used to calculate the deflection at any point on the beam.