Problem 10.4-3 A propped cantilever beam of length 2L with support at B is loaded by a uniformly distributed load with intensity q. Use the method of superposition to solve for all reactions. Also draw shear-force and bending- moment diagrams, labeling all critical ordinates. MA L. Solution 10.4-3 Select Ry as redundant. (8g), = Deflection at B due to force Rg RELEASED STRUCTURE AND FORCE-DISPLACEMENT RELATIONS (8g)2 ЗЕ FROM COMPATIBILITY EQUATION 17 (SB) = (8g)2 .. RB 7b- EQUILIBRIUM RA = 2qL – RB (1) MA = 2qL? – RgL = --qL² (2) (8g), = Deflection at B due to uniform load q 17qL (8g) * 24EI My Question: HOW DO YOU GET THIS. I know how to solve the problem after this step, but how is this deflection formula derived? Using a table? What is it! Please explain in as much detail as possible!

Problem 10.4-3 A propped cantilever beam of length 2L with support at B is loaded by a uniformly distributed load with intensity q. Use the method of superposition to solve for all reactions. Also draw shear-force and bending- moment diagrams, labeling all critical ordinates. MA L. Solution 10.4-3 Select Ry as redundant. (8g), = Deflection at B due to force Rg RELEASED STRUCTURE AND FORCE-DISPLACEMENT RELATIONS (8g)2 ЗЕ FROM COMPATIBILITY EQUATION 17 (SB) = (8g)2 .. RB 7b- EQUILIBRIUM RA = 2qL – RB (1) MA = 2qL? – RgL = --qL² (2) (8g), = Deflection at B due to uniform load q 17qL (8g) * 24EI My Question: HOW DO YOU GET THIS. I know how to solve the problem after this step, but how is this deflection formula derived? Using a table? What is it! Please explain in as much detail as possible!

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter10: Statically Indeterminate Beams

Section: Chapter Questions

Problem 10.4.27P: A beam rests on supports at A and B and is loaded by a distributed load with intensity q as shown. A...

See similar textbooks

Similar questions

A simple beam with an overhang is subjected to d point load P = 6kN. If the maximum allowable deflect ion at point C is 0.5 mm, select the lightest W360 section from Table F-l{b) that can be used for the beam. Assume that L = 3 m and ignore the distributed weight of the beam.
A fixed-end b earn is subjected to a point load at mid-span. The beam has a rectangular cross section (assume that the h/b ratio is 2) and is made of wood (E = 11GPa). Find height h of the cross section if the maximum displacement of the beam is 2 mm. Calculate the displacement of the beam at the inflection points.
The deflection curve for a cantilever beam AB (sec figure) is given by v=q0x2120LEI(10L210L2x+5Lx2x3) Describe the load acting on the beam.
A simple beam AB of length L and height h (see figure) is heated in such a manner that the temperature difference 7= T{between the bottom and top of the beam is proportional to the distance from support A: that is, assume the temperature difference varies linearly along the beam: T2- Tt= Tax in which 7"0 is a constant having units of temperature (degrees) per unit distance. Determine the maximum deflection SW9Xof the beam, Repeat for a quadratic temperature variation along the beam, so T2+T1= Tax
A cantilever beam JA of length Land height/; (see figure) is subjected to a temperature change such that the temperature at the top is 7[ and at the bottom is 7. Determine the equation of the deflection curve of the beam, the angle of rotation BBat end and the deflection 8Bat end B,
A propped cantilever beam, fixed at the left-hand end A and simply supported at the right-hand end B, is subjected to a temperature differentia] with temperature T1on its upper surface and T2on its lower surface (see figure).
A simple beam ABC DE supports a uniform load of intensity iy (see figure). The moment of inertia in the central part of the beam (BCD) is twice the moment of inertia in the end parts (AB and DE). Find the deflection Scat the midpoint C of the beam. (Obtain the solution by using the modified form of Castigliano's theorem.)
A heavy object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see figure). Obtain a formula for the maximum bending stress ^ma* due to tne filing weight in terms of h, st, and 5st, where it is the maximum bending stress and Sstis the deflection at the midpoint when the weight W acts on the beam as a statically applied load. Plot a graph of the ratio o"max/ö"it (that is, the ratio of the dynamic stress to the static stress) versus the ratio iifS^r(Let h/S^ vary from 0 to 10.)
A simple beam ACB supports a uniform load of intensity q on the left-hand half of the span (see figure). Determine the angle of rotation ÔBat support B>(Obtain the solution by using the modified form of Castigliano's theorem.)
A two-span beam with spans of lengths L and L/3 is subjected to a temperature differential with temperature T1on its upper surface and T2on its lower surface (see figure). Determine all reactions for this beam. Use the method of superposition in the solution. Assume the spring support is unaffected by temperature. What are the reactions when k ?
A symmetric beam A BCD with overhangs at both ends supports a uniform load of intensity q (see figure). Determine the deflection SDat the end of the overhang. (Obtain the solution by using the modified form of Castiglianos theorem.)
A beam rests on supports at A and B and is loaded by a distributed load with intensity q as shown. A small gap exists between the unloaded beam and the support at C. Assume that span length L = 40 in. and flexural rigidity of the beam EI = 04 x 109lb-in2. Plot a graph of the bending moment at B as a function of the load intensity q. Hint: See Example 9-9 for guidance on computing the deflection at C.