# What is Beam deflection: Definition and 75 Discussions

Beam deflection tubes, sometimes known as sheet beam tubes, are vacuum tubes with an electron gun, a beam intensity control grid, a screen grid, sometimes a suppressor grid, and two electrostatic deflection electrodes on opposite sides of the electron beam, that can direct the rectangular beam to either of two anodes in the same plane. They can be used as two-quadrant, single-balanced mixers or (de)modulators with very linear qualities, their mode of operation similar to one-half of a Gilbert Cell, by applying an unbalanced signal f1 to the control grid and a balanced signal f2 to the deflection electrodes, then extracting the balanced mixing products f1 − f2 and f1 + f2 from the two anodes. Similar to a pentagrid converter, the cathode and the first two grids can be made into an oscillator. Two beam deflection tubes can be combined to form a double-balanced mixer.
They need extensive shielding against external magnetic fields. The ballistic deflection transistors currently under development employ a similar principle.

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1. ### Simply supported beam with a spring support in the middle - deflection

Hi, I'd like to calculate the maximum deflection of a simply supported beam with spring support in the middle and UDL (uniformly distributed load) acting on the whole beam: Here's my derivation, starting from the known formula for maximum deflection of a simply supported beam with UDL and no...
2. ### Beam deflection and curvature radius formula doubts

Hi, I am working with leaf springs and studying the derivation of the formula for the deflection of such a structure. The derivation is shown here: My only doubt is how to obtain the following formula: $$\delta=\frac{L^{2}}{8R}$$ where: ##\delta## - deflection, ##L## - length of the beam...
3. ### Lessons with electron beam deflection tube and teltron tube

Hello, I would like to discuss with my students the deflection of electrons in electric and magnetic fields. For this purpose, I would like to perform the experiments with electron beam deflection tubes and teltron tubes. How would you implement this organizationally in the classroom? There are...
4. ### I Base Motion and Vertical Beam - Basic Reaction Forces?

So I am trying to understand how to estimate the amount of deflection [D] the vertical beam shown above would experience if the base it is attached to is accelerating at a constant acceleration [a] of 9.81 m/s. I assume the Force [F] would be equal to weight of the vertical beam (mass x...
5. ### Choosing correct steel beam for a span

I have a weight of 30,000 lbs distributed across a span of 100' and supported at the ends. If I have 3 beams to support this load, each beam would then need to hold 10,000 lbs, and with a F.S of 1.6 each beam would need to hold 16,000 lbs. If I assume my max deflection at 1", then I can find the...
6. ### A500 steel tubing beam deflection

Hello, I'm looking to construct a simple rectangular 13'x17' hollow steel frame over my patio, but I'm getting conflicting beam deflection calculations. I need to determine my beam size for my long spans of 17'. My plan was to use 3.5"OD A500 structural steel. 11 gauge (.120 in) wall...
7. ### Cantilever beam deflection with point mass and point load at the end

Hi all, I was looking for help with obtaining deflection at end of a cantilever beam with point load at end as well as point mass at the same location. I believe it would be exactly same. Is this correct? That is, I think just adding point mass at the cantilever's end wouldn't change the...
8. ### (Matlab) beam deflection solution using symbolic simultaneous equations

I have tried to searched for functions online and apply it, but still it does not work well. May I ask how can I solve symbolic simultaneous equations with Matlab? Or is there anything went wrong with my program? Homework Statement Consider a stepped beam shown in below. The beam is...
9. ### Solving Beam Deflection with Singularity Equations

Homework Statement Homework Equations Singularity equations for beam deflection $$\sum M_B=0=-M_0-R_AL-M_0$$ $$R_A=-\frac{2M_0}{L}$$ The Attempt at a Solution I know how to use singularity equations and all that but my problem is calculating the force especially when moment is involved. For...
10. ### How Do You Calculate Beam Deflection for an I Beam on Lorry Trailers?

Hello, I am looking for some advice on calculating the beam deflection on a setup described below. There is an "I Beam" sitting across the back of two lorry trailers with a uniformly distributed load in the middle of the beam. I am slightly confused as to what type of support this would be if...
11. ### Deflection of Tapered Beam with Elliptic Cross Section

I am working on deriving expression for deflection of a tapered beam with an elliptic cross-section. Hence, area moment of inertia is a linear function of the beam length. The beam is fixed at one end, and a concentrated force F is applied on its tip at the free end. I am using the known...
12. ### Closed form solution for second order beam deflection?

Homework Statement A beam of length L is fixed on one end and roller supported on the other end. An axial force P is applied on the ends of the beam. The beam is loaded with a uniform distributed load (q) along its entire length. The beam has constant EI. Find an expression for the maximum...
13. ### Beam Deflection Homework: Missing Moment Calculation for Beam Circled Section

Homework Statement for the circled part, why the why the author didnt include -12(9)kNm moment in the equation of moment ? [PLAIN]http://imgur.com/a/l3Bu4http://imgur.com/a/l3Bu4 Homework EquationsThe Attempt at a Solution IMO, the author should include it in the equation, am i right? So, M=...
14. ### Beam Deflection Homework: Finding Centroid Distance from Point B

Homework Statement http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/solution-to-problem-625-moment-diagrams-by-parts) from the link , why the distance of centroid from B is (4/3) and (9/4) as shown? Homework EquationsThe Attempt at a Solution it should be (4- (2/3) ) and...
15. ### Beam Deflection: Solving for Unknowns at a Given Point

Homework Statement determine deflection of beam Homework EquationsThe Attempt at a Solution at x=0, y=0 , i found that C2 = LP(a^2)/6 (circled part) but the author gt 0, which is correct?
16. ### Beam deflection integration help

Homework Statement can someone explain about the RHS of EIy' and EIy'' ? how to get the RHS of EIy" from RHS of EIy' ?? It's not integration of dx , am i right? Homework EquationsThe Attempt at a Solution if it's integration of dx, it should look like this , right?[/B] EIy' = 0.25P(x^2) -...
17. ### Beam Deflection: Solving with EI w''''(x) = q and Boundary Conditions

Can the deflection curve of the beam in picture be solved by using the following approach: https://dl.dropboxusercontent.com/u/104865119/beam2.PNG 1) EI w''''(x) = q 2) Integrate four times, solve the constants from boundary conditions (deflection and moment zero at the supports) Thanks...
18. ### Calculating deflection with rotation about center support

I am preparing for a qualifying exam for my PhD program and am looking at some of the old tests from previous years (as supplied by the school for study/prep material). I have come across a deflection problem that has me stumped, and I might just be overthinking it. The problem:
19. ### Method to calculate beam deflection

How do you get deflections of a fully restrained beam? :) I already solved for the propped reactions and end moments.. I'm not sure how to do that part. :/ ありがとうございます。 :)
20. ### Why Is the Slope of a Beam Zero at Its Midpoint Despite Maximum Deflection?

Can someone explain why the slope dy/dx = 0 at x = L/2? L/2 is the midpoint and there would be a deflection here so surely the slope of the deflection curve shouldn't be 0? I'm finding it hard to visualise this. EDIT: I think I understand the above. The slope of the deflection curve at x = L/2...
21. ### Beam Deflection equation question

regarding this equation, δ=(PL^3 )/(48EI) For the calculation of maximum deflection, if my structure is not longer a full form beam (meaning the structure has 6 holes drilled to it), can this formula still be used?is...
22. ### Beam Deflection with single support

Hello I am trying to setup a problem to represent a pipeline crossing over another perpendicular pipeline on the seabed. I am trying to represent the problem as a simple beam and having some issues with the supports i am selecting and the boundary conditions. Attached is a picture representing...
23. ### Nonlinear Mass Spring Damper with Euler Bernoulli Beam

I'm trying to find a solution to a system in which a clamped free Euler-Bernoulli Beam system rests on top of a mass-spring-damper system. The MSD system has nonlinearities in both the spring and the damper and is of the form: I have extended the nonlinear restoring force to its 3rd term and...
24. ### Simple beam deflection and center load

Homework Statement http://www.upload.ee/image/4762203/DSC_0009_1_.JPG I need to find the formula which is in the red circle. Beam is simply supported at both ends and there is center load. Do you think that this is correct? Homework EquationsThe Attempt at a Solution
25. ### Continuous beam deflection (structural)

Homework Statement Using continuous beam theory, constructing BM diagram from points b to c, to calculate the max deflection. I only found a have a single solution, though the BM digram show two points of zero bending. I can provide the solution. [edit: Rb = 685 N] Homework Equations...
26. ### Constructing a Bending Moment Function Using McCauley's Method

I have A beam of 1.2 m long, supports at 0m and 0.8 m. forces of 10 N at 0.4 m and 5N at 1.2 m I need to find the deflection equation for this situation. Can someone have a look and see if they can come up with the equation. As I have tried but my results do not match what I am expecting
27. ### Solving a Laser Beam Deflection Problem Using Equations

Dear all, I have pretty simple problem in terms of understanding but I can't write an analytical solution. Consider you have a laser beam (without divergence, single wavelength). You can see the intensity distribution on the screen perpendicular to the beam. Then you insert a thin glass layer...
28. ### Plotting a Beam Deflection Graph

Homework Statement I need to plot a graph showing the deflection of the beam across its length giving a value of x at every 1m. The youngs modulus for the beam is 210 GNm^-2 and the moment of inertia is 54 X 10^-7 m^4 Homework Equations Really unsure where to start on this one. I have found...
29. ### Simply supported deep beam deflection

Hi, I have a problem with simply supported deep beam which has a uniformly distributed load. The beam is simply supported at both ends but I have to consider the results for the following 3 scenarios - where the support is at the bottom of each end of the beam - where the support is at the mid...
30. ### Maximum Bending Stress in Cantilevered Steel Channel Beam

Homework Statement Okay this is the problem I have: I have a Steel Channel beam which has an cross sectional height of 300mm. It is 150mm in depth. Its wall thickness is 20mm. This beam is 6meters long as has a 10kN/m UDL applied. It is fixed at one side and unsupported at the tip. I have...
31. ### Help with beam deflection problem

I need help with this beam deflection problem for 1 the book my professor gave me almost everything is hand written including the beam stuff... SO I can't read it at all and its really frustrating trynna do this without being able to read the formulas or anything please helpp! I attached the...
32. ### Deriving Moment & Elastic Curve Equations for Incomplete Triangular Load on Beam

I was wondering how you would derive the moment and elastic curve equations for an incomplete triangular load. Say you have a pin at the left end of the beam and a roller at L/2 from the left, and a triangular load that goes from the pin and ends at the roller. I know you have to do some kind of...
33. ### Beam deflection boundary condition calculation

Homework Statement Find the deflection at x=L/4 and x=L/2 for the beam Homework Equations See attached pic. The Attempt at a Solution So I have the solution derived in class. Only 0<x<L/2 is derived because since the load on the beam is at L/2, the equation is valid for the...
34. ### Technology methods and analysis - Beam Deflection Problem

I just started my Mechanisms and dynamics class today for engineering. We already got the first assignment that's due in a day or so. The assignment consists of only 3 questions but first one is totally confusing me and I don't know what to do about it. I emailed the instructor 10 hours ago and...
35. ### Maximum Beam Deflection: How to Find and Locate It | Homework Help

Homework Statement FIND MAXIMUM DEFLECTION AND ITS LOCATION (PLEASE SEE THE FIGURE)... THANKS Homework Equations The Attempt at a Solution
36. ### Beam Deflection in a Tapered Pipe

I need help comparing the deflection of pipe with two different cases. Case 1 is a regular non-tapering pipe. The case 2 is a tapered pipe that should deflect less than the straight pipe. I am working in MathCad and can change the value of my variables, so I have set the two cases to be equal...
37. ### How Do You Calculate Deflection in a Simply Supported Overhanging Beam?

Hey all, first post! Looking to find a deflection equation for a simply supported overhanging beam with two supports and a point- load at the end of the canteliever. I can determine reactions at the supports but i am having trouble finding deflection between the supports. Any help is...
38. ### How do I determine the K value from a cantilever beam deflection test?

Hi, I am new to this type of material and am hoping that someone may be able to assist me. In short I am putting a cantilever beam under test to determine its bending moment and stiffness (K value) in order to get a strain reading that can be related to an exact model in solid works. The...
39. ### Calculating Beam Deflection using Double Integration

Homework Statement If the distributed force is removed from the beam in the picture attached and not considered, calculate the deflection at point D. Homework Equations Double integration for deflection [V] The Attempt at a Solution Moment = Ra*x-P(x-3*L) = Slope =...
40. ### Exploring Beam Deflection: Area Moment, Moment of Inertia & Center of Gravity

Homework Statement Hey In my assignment I am writing about beamdeflection, but there's some things i really can find out how to do. I need to explain area moment, moment of inertia and the center of gravity, i need to explain this with the help of integration. Under her I've inertet...
41. ### Calculation of Bending Moments and beam deflection

Homework Statement The picture of the beam below has a module of rigidity EI, determine the reactions at the supports and the equation of the deflection curve of the left half of the beam Homework Equations v*EI=((Ma*x2)/2)+((Ra*x3)/6) Ʃ of Forces in Y direction = Ra+Rb=0 Ʃ Moments...
42. ### MHB Max Beam Deflection: Find $x$ Value for $D$

The deflection D of a beam of length L is $D=2x^4-5Lx^3+3L^2 x^2$ where $x$ is the distance from on end of the beam. Find the value of $x$ that yields the maximum deflection. this is from a unit on inflection points so assume this is $\frac{d^2}{dx^2}$ and also looks like an implicit...
43. ### Tapered cantilever beam deflection and stress distribution

Homework Statement A positive moment of 12000Nmm at the tip applied as two equal and opposite point loads of 1000N in the x direction at C and D. The beam is fully fixed along AB. Young's modulus E = 200*(10^3) MPa and the poisson's ratio = 0.3. Geometric Properties: Width, b=10mm...
44. ### How can I use integration to find the maximum deflection in a beam?

Homework Statement Find the maximum deflection in the beam. E=205Gpa Beam breadth = 195mm UDL on beam: 40 Bar Homework Equations I have useed the method of superposition to try and solve it. Is this the best way? It has been suggested that finding the displacement by integration would...
45. ### Perpendicular Beam Deflection question

Homework Statement Given a W21x68 beam with 1.388 kips per foot loading spanning 34 feet. The beam will carry the load but the maximum deflection is greater than wanted. We would like to put a W33x118 beam perpendicular to the centerline of the W21x68 (17 feet), to limit the deflection...
46. ### Analyzing Beam Deflection in Complex Loader Arm Structures

Hi, I haven't done beam deflection before. My textbook shows the usual simple beams with a perpendicular force acting on it. This one is a lot more complicated. I'm pretty sure the forces acting in the horizontal direction have to be added into this some how. Can someone look at the...
47. ### Please i with Beam Deflection problem

Can anyone help me to find the answer,,, its a very difficult question! Q- calculate the safe inclusive UDL for a 356x171 UB67 simply supported at the ends of span of 9m. The permissible bending stress is 167N/mm*2 and the defluction must not exceed (1/360) x span, and I = 187.2x10*6mm*4...
48. ### How Do You Calculate Deflection in Double Beam Assemblies?

Hello, I would like to know how to find the deflection of simple 2 beam assemblies. In college, I remember only doing one beam problems. For example, a beam supported at both ends with a load in the center would follow the equation v_max= -(P*L^3)/(48*E*I). What if 2 identical beams...
49. ### Solidworks beam deflection and MDSolids

Hi all Sorry if this is in the wrong place... I've been doing some beam deflections on a simply supported beam, with loads applied to the overhangs, and have used MDSolids, Hand Calculations and Solidworks. My hand calculations match up with the results that I have got from MDSolids...
50. ### Calculate beam deflection at 1m intervals

Am i right in saying i can use this formulae: - W/EI((x^3/12) - (xL^2/16)) + w/EI((Lx^3/12) - (x^4/24) - (xL^3/24)) please help. See attached question. Question aii. Thanks