# What is Cantilever: Definition and 233 Discussions

A cantilever is a rigid structural element that extends horizontally and is supported at only one end. Typically it extends from a flat vertical surface such as a wall, to which it must be firmly attached. Like other structural elements, a cantilever can be formed as a beam, plate, truss, or slab.
When subjected to a structural load at its far, unsupported end, the cantilever carries the load to the support where it applies a shear stress and a bending moment.Cantilever construction allows overhanging structures without additional support.

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1. ### Gussets and cantilever bending

Do gussets perform well in cantilever bending when horizontally oriented, as opposed to vertically oriented? I assume vertical orientation performs well in bending, in which you can calculate the area moment of inertia by adding that of the gusset cross sections individually, and the joint helps...
2. ### Engineering Need help in solving SDOF cantilever

1.) I'd calculate the force needed to deflect the beam by using the method of virtual work for t=0 which is u[L] = FL^3/3EI. From there on I am completely clueless. 2.) Task is to calculate damping, mass and stiffness of the SDOF by using the data sheets which is basicly the u''(t) function of...
3. ### Elasticity of a Tubular Cantilever Beam

I have a problem where I have a metal tube that I am modeling as a cantilever beam which is fixed at one end and has a point load at the other end. The material of this beam is 304 stainless steel, the inner diameter is 0.5mm, the outer diameter is 2mm, and the length of the beam is 4.15mm. With...
4. ### What would be the ideal cross section of an axially loaded cantilever beam?

Pretty much the title. Just some brain teasers I'm trying to figure out. I can't think of how a cross section would come into play when it comes to axial loading. Buckling? Since the critical force for buckling is proportional to moment of inertia, so theoretically if I have a high moment of...
5. ### Construction Aluminum Cantilever for Truck Camper

(Continuing from the summary...) I want to build this safely, so I am putting this out here for expert advice. My choice for the shape for the aluminum cantilever is angle, T, square tubing or round. The foam is 2” thick, so I’d like to keep the supports at 2” in width and height. I need to...
6. ### Engineering Cantilever Modeling System - Help requested please

Please see question attached. I am really stuck on this.
7. ### Engineering Cantilever and encastré beams: bending moment and shear force

I have to discuss the Bending moment and shear forces in cantilever and encastré beams. Does anybody know of good websites showing that is simple to understand showing. All i can find is how to calculate and bending moments and shear force digrams which don't really understand. Can...
8. ### Bending of a cantilever plate

Hi, books such as „Roark’s Formulas for Stress and Strain” or Timoshenko’s „Theory of plates and shells” provide formulas for maximum bending stress and deflection for many cases of rectangular plates. However, I can’t find a simple case of a cantilever plate (one edge clamped, all other edges...
9. ### Harmonic forced vibration of a cantilever beam

Hi, in the book titled "Formulas for Dynamics, Acoustics and Vibrations" by R.D. Blevins, I've found a formula that can be used to calculate the bending stress in a cantilever beam subjected to harmonic force applied at the free end. The formula looks like this: \sigma=\frac{F_{0}Ec}{m...
10. ### Cantilever Beam Calculation

Hi, I am trying to figure out how many 1" steel square tubing pieces it would take to support a 500lb weight extended out 40" on a cantilever. I have seen Modulus of Elasticity figures ranging from .029 GPa to 200 Gpa for Steel. The steel I plan to use would be common hot rolled square tubing...
11. ### Deflection of a cantilever beam with applied tension at the free end

Not much to add since the question is fairly simple, but again I'm wondering if applying tension at the free end of a cantilever beam affects the deflection it would have if only itself weight is considered. Intuitively, tension should tend to straighten the beam, and if it does, how to...
12. ### 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...
13. ### Vertical Cantilever Slurry Pump Critical Speed

Hello all, I am an engineer with a manufacturing company and I am working for calculating the critical speed for a vertical cantilever slurry pump. This pump design includes one ball bearing and one taper roller bearing within the bearing housing. Then the shaft extends vertically downward...
14. ### Simplified Tapered Cantilever Beam Generalizations

I looked in Roark's Formulas and didn't find anything. Basically, I design parts that need to bend. Mostly plywood and plastic. Mostly cantilever beams. I like to taper the beams so that the stress along the beam is more uniform. The question I have is how much do I taper. With no taper, the...
15. ### Moment of inertia of a branched cantilever beam

Hey there! I am working on a project concerning the mathematical modeling of nano-swimmers in a viscous medium. Assuming the nano-swimmers to be cantilever beams, the project involves calculation of moment of inertia of the said nano-swimmers. While calculating the moment of inertia of a simple...

Hello, everyone. I have been trying to understand the meaning of the question from the posted image. I think that preloading has to do with adding bolts to the cantilever beam such that it can withstand the force from above, but I am not sure how exactly these bolts should be implemented...
17. ### Pure bending of a perfectly elastic cantilever beam

Hi, My question is: If a constant load is applied at the free end of a perfectly elastic cantilever beam, would the beam oscillate about a mean position? Or would it eventually come to rest at the equilibrium position? There are no damping effects. Thank you.
18. ### Off-Axis Torque To A Cantilever Beam

I'm interested in understanding how to deal with a torque applied to an angled cantilever beam. The torque is being applied along a horizontal axis at the location of the end of a cylindrical beam. I am interested in how this torque will cause twist along the beam's axis, as well as any...
19. ### Using Macaulay's method of deflection on a cantilever beam

Homework Statement i) Determine the slope of the beam 1m from the wall. ii) Calculate the deflection at the free end of the beam. Homework Equations Macauly's method of deflection: M = -RX + W[X-a] Integrate once for slope Integrate twice for deflection The Attempt at a Solution [/B] It...
20. ### When does a cantilever beam fail in reality?

Hi, like the title says, how do we actually calculate when a cantilever beam fails in reality? We’ve been taught that these are absolutely fixed to the ground. However, in reality these would probably be bolted onto the ground, so how do we calculate the force trying to lift the fixed beam on...
21. ### Negating the cantilever effect for this latching mechanism

Please excuse my poor explanation in advance, I'm not an engineer. I have a latching mechanism that has an off center piston and needs to get actioned from a 'cantilevered' position. Please see attached (crappy) sketch of desired effect vs real world behaviour. Is there any solutions to negate...
22. ### Cantilever Bridge/Crane

I am doing an engineering project and my team has been assigned to build a cantilever which should be able to hold 5kg minimum, 1 m away from the base. I will be using thin wood pieces, PVA glue, and string with the restrictions: height 60 cm, length 1.25 m, width, 20 cm. I have an idea of...
23. ### Cantilever beam deflectiom

Homework Statement The Figure shows a welded steel bracket loaded by a force F = 5 kN. Homework Equations [/B] The Attempt at a Solution I know that the total deflection is the deflection of the beam due to F. And I also need to take into account the angular deflection at the joint...
24. ### Castigaliano's Theorem for cantilever beams

Homework Statement Hi I am trying to derive an expression for the deflection in a cantilever beam using castigliano's theorem. I have found and attached an example of the solution. I understand the most of what is going on in the attached solution but I don't know where the b^3 came from in the...
25. ### Castigaliano's Theorem for cantilever beam

Hi I am trying to derive an expression for the deflection in a cantilever beam using castigliano's theorem. I have found and attached an example of the solution. I understand the most of what is going on in the attached solution but I don't understand where the b^3 came from in the last line.
26. L

### Effective Flexural Rigidity (EI) of Composite Cantilever Beam

Hello, I am trying to derive the (Euler-Bernoulli) beam equation of a composite beam to determine the vibration and natural frequencies (up to 3 modes) of the beam. The composite beam can be modeled as in the picture below: In order to apply the general equation: (EI)effw'''' = m'eff...
27. ### Sign convention of fixed end moment at cantilever beam

Homework Statement I don't understand why the fixed end moment at AE is 10KNm ( clockwise) . Homework Equations The Attempt at a Solution Forger about the sign convention here , i have the resultant moment = 10KNm , which ic clockwise , why in the 2nd picture ( SFD and BMD part) , the...
28. B

### Critically damped cantilever beam

I need to design a multi-layer cantilever beam with alternate visco-elastic and elastic layers. The goal is a beam with 18" unsupported and 4" glued to a firm support. In operation, this firm support will be vibrating in the audio range and the beam wants to damp out those vibrations and not...
29. ### Vibrations in cantilever beams

Hi fellow mechanical engineers, I am designing a rather simple excel program for work that deals with vibrations in robots. Imagine a robot that is made up of linear axes that can move in x,y,z sort of like a 3D printer, take a look at this picture: https://pasteboard.co/8hvV5vf.png Focusing...
30. ### Building metal rv cover with cantilever

Good morning everyone, new member. Have been reading some other posts for awhile. I am auto technician/business owner. I was wondering if I was to post some rudimentary plans for a rv cover I am going to build over a 2 post outdoor car lift, if some one would be willing to give me points on any...
31. ### Vibration of a cantilever beam problem

Homework Statement A rectangular cantilever beam of length L and side lengths b with negligible mass is attached horizontally to a wall. A mass m is attached to the end of the beam where a motor is also located. The motor applies a force on the end of the beam described by the equation...
32. ### Statics - Cantilever Beam

What's happening Form, It's been a while since I've done a FBD, but I wanted to get someone's input here and tell me if my math/logic is correct. I want to install a cantilever steel beam with a 20 lb mass at the end of it. I'm using carbon steel ASTM A108 (cheapest steel on McMaster-carr). I...
33. ### Why are there modes in cantilever beam oscillation equations

I'm doing an experiment measuring the relationship between length of a cantilever beam and period of oscillation when I twang it on one end, but I can't seem to understand the equation. The equation for measuring frequency is given here:https://www.hindawi.com/journals/amse/2013/329530/ but I...
34. ### Designing Haunch for Cantilever Beam in BS 8110

Hi guys, how do I design the haunch for the cantilever beam? The slab area is relatively small, with 125thk ( 4.39m x 1190m ). I've looked through everywhere but I can't find on how to design the haunch. I'm using BS 8110. Thanks.
35. ### Cantilever Pipe Assembly - Statics

To simplify my situation, I am installing a horizontal cantilever pipe (30” length, 3” nominal diameter) which will be connected to a vertical pipe (3” nom diameter, acting as the wall) by a T-connection. See the diagram below. At the end of the cantilever the pipe bends up at 90 degrees for...
36. ### Vibration in "cantilever" rotating bar

Hi. I'm working in the design of an auotomatic bar feeder for a CNC lathe. I've established that the bars will not be longer than 1.2 m and will not have a diameter of more than 75 mm. Suppose they are steel bars, which would make them have a mass of about 80 kg So, bars are tightly held in one...
37. ### Cantilever Beam problem

A cantilever beam at low frequency behaves like an underdamped 1 DOF mass/spring/damper system. We are trying to find the roots of the Characteristic equation which are lambda1,2 = -dampingRatio x wnatural /sqrt(1-dampingRatio) Relevant formulas and given values: damping ratio = c/2sqrt(m/k)...
38. ### Moments and force -- Forces on a cantilever hole punch

Homework Statement sam makes a punch hole with the perforater( two holes ). She presses the lever at A down with a force of 40 N. Calculate the total force which a single pin presses on the paper. Homework Equations http://s6.postimg.org/yx62wbild/image.png The Attempt at a Solution would it...
39. ### Calculating Bending Stress for a Cantilever Beam

Hi, I'm trying to calculate bending stress for a cylindrical beam. I'd like to have my result double checked because I got an answer that doesn't make sense to me. All of this is personal research, so I'm not very confident in my answer. It's a cantilever beam with a point mass of 347.4 oz. on...
40. ### Deflection of cantilever

Homework Statement in the notes , i don't understand the circled part . I don't understand why the circled part moment M is in anticlockwise direction ... Shouldnt it be in clockwise direction ? Homework Equations The Attempt at a Solution As we can see , the P at the one end will cause the...
41. ### Airy's stress function for a cantilever beam

I have to calculate Airy's stress function for a cantilever beam made of two different material along its length. The young's modulus of the first half is E1 and E2 for second half. The beam is made such that these materials are joined to each other one after other along its length. At the...
42. ### Cantilever Beam Small Deflection Approximation

I am calculating the strain in a cantilever beam with a point load for a given deflection. The deflection is around .5mm for a beam that is just over 5mm long (width is 3.8mm and height is 0.15mm). I was told for the assumption of small deflections to be valid, deflection should be 2% of the...
43. ### Deriving Strain in Cantilever Beam with Known Deflection

I am trying to derive the strain at the base of a cantilever beam with a known deflection. I know the bending stress is equal to Mc/I, so the strain is Mc/IE, where c is the distance from the neutral axis. For a point load ,P, the strain would then be PL/IE. Since the deflection is known I...
44. ### Strain of a Cantilever beam

Hi, Well i have a system with a excited (in y axis) cantilever beam. I struggling to obtain a expression that gives the strain based on the dislocation y. I know that the displacement of the beam is given by: Ya=PL^3/(3EI) but how i make a correlation between this and the strain of the...
45. ### Offset Cantilever Beam - Horizontal & Vertical Deflection

Homework Statement The offset cantilever beam, ABCD, is fabricated from structural steel. Es = 30,000,000 lbs/in2, I = 60 in4. A load of 2000 lbs is placed at point D. Neglect the weight of the beam. Determine the horizontal and vertical deflection at D with respect to A in inches. Homework...
46. ### Deflection of a Cantilever with support

I sketched out a slightly simplified model. It is a cantilever rod with two supporting rods of slightly larger diameter, connected by a plate. (Ignore the weight of the individual parts. For illustration purposes, I draw this to resemble a cantilever beam from the side view but in actual design...
47. ### Machine malfunction due to Cantilever design

Hello all! I work for a machine design & manufacturing firm. We also do machine repairs & refurbishing work. We currently have taken up a project where-in an we have to solve a critical problem in an automatic part washing machine. The machine is a multi-stage concept, wherein the parts are...
48. ### Solve Cantilever Question: Mechanical Engineering Student

Hey guys, first-year Mechanical Engineering student here and a new forumer of this site too. I got a static question that I need help with. Question: Relevant Equations: Sum of all forces in the y direction = 0 Sum of all moments = 0 Attempted Working: I just need help finding the...
49. ### How to solve the large deflection of the cantilever beam

how to solve the large deflection of the beam, i have tried using finite element method but unable to find it.
50. ### Increasing Cantilever Beam Stiffness

Is it possible to create a cantilever beam with constant or increasing stiffness. I've been experimenting with several different shapes and profiles, and have not had any luck. I know that there are shapes with constant stress throughout, but I'm hoping to find a shape with constant or...