What is Cantilever beam: Definition and 133 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. mechanic667

    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...
  2. Johnstonator

    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...
  3. FEAnalyst

    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...
  4. R

    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...
  5. M

    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...
  6. K

    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...
  7. fpjeepy

    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...
  8. Sonic Tseh

    Calculate the reduction in the deflection at the free end

    I can solve the deflection if only cantilever beam by deflection formula, but i have no idea for this question if calculated with a cable support arrangement.
  9. D

    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...
  10. J

    Simple Question - Preloading of a Cantilever Beam

    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.I would...
  11. S

    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.
  12. A

    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...
  13. K

    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...
  14. T

    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...
  15. Jeviah

    Does the angle of a beam fixed at two points affect the method?

    Homework Statement if a beam fixed at two points is on an angle say 45 degrees from the x or y-axis instead of running parallel to x-axis in most questions does this effect calculations? The force acting upon it would be a load directly downwardsHomework Equations N/A The Attempt at a Solution...
  16. H

    Calculating Angular Deflection in a Welded Steel Bracket

    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...
  17. H

    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.
  18. 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...
  19. F

    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 EquationsThe 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 moment...
  20. B

    Introducing Gary Nelson aka BeamStudent

    I hope to design and build critically damped cantilever beams for a musical instrument transducer application. I have a PhD in EE (1972) and am not well versed in stresses and strains, but see that I need complex modulus of visco-elasticity. I'm searching for tools to do this kind of analysis
  21. 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...
  22. Feodalherren

    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...
  23. N

    Can a Cantilever Beam with a 20 lb Mass Hold Up without Failing?

    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...
  24. A

    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...
  25. H

    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.
  26. Andrew VanFossen

    Moment of Inertia: Non Uniform Rod

    Homework Statement Hello, I am looking to determine the moment of inertia for the cantilever beam pictured below. I want I to be a function of L1 and T1. Known variables: L, D, P, t Dependent variables: T2, L2 Design variables: T1, L1 Homework Equations L2 = L - L1 T2 = T1 - t Standard...
  27. K

    Cantilever Beam Stiffness Calculation

    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)...
  28. N

    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...
  29. Divya Shyam Singh

    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...
  30. R

    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...
  31. R

    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...
  32. G

    Correlating Displacement and Strain in a Cantilever Beam System

    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...
  33. M

    What is this and where can I find a replacement

    The square seat (?) for the accelerometer has started to fall apart and I need to find a replacement for it. If this helps, the accelerometers are placed equidistant apart from each other, and the tester hits it - the cantilever beam - with a mallet to simulate vibration. Please refer to the...
  34. M

    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...
  35. Firzan

    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...
  36. cvnaditya

    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.
  37. J

    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...
  38. cvnaditya

    Deflection of cantilever beam having two Young's modulas

    what is the formula for the cantilever beam having two different young's modulas and moment of inertia, when a point load is acting on the free end. i have been trying but unable to get the formula. if the formula i can validate my project work and complete it
  39. C

    Deflection in a Cantilever beam

    Hello, i was looking for ways i can reduce the deflection in the cantilever beam whose one end is fixed and load is applied at the free end. Few i thought of was, 1- Reducing the length of the beam 2- Increasing the modulus of elasticity of the beam 3- ?? 4- ?? 5...... Appreciate your help...
  40. Vircona

    Cantilever Beam Failure: Help?

    Hey, all, So I posted a similar thread yesterday about my project design issue, but I've made progress on it by taking a different approach. For the project, I have a cantilever shaft of fixed length (1.2m) and a tensile axial loading, and two torsional loadings in the same direction at...
  41. T

    Calculating Deflection and Stress in a Tapered Cantilever Beam

    Hey all, So I have this beam problem and I honestly am lost with it! The beam is I-section cantilever, tapers in depth along its length (See picture attached) with a point load at the free end. I am trying to figure out the deflection formula and how to derive it! Also, when calculating its...
  42. T

    Vibration of a cantilever beam

    Hi there! Im trying to do an analysis in Abaqus of a cantilever pipe, with a tip mass at the free end, that is decelerating to a stop at 10 m/s2 from 10m/s, causing it to vibrate. To validate my results I am doing some handcalcs. I have done a static analysis and calculated the maximum...
  43. R

    Stress at crack tip of a 2D cantilever beam under sinusoidal excitation

    I need some information urgently. I am working on crack of a 2-D cantilever beam. One side of the beam is fixed. I am applying a sinusoidal time varying load on other end in Y-direction.Beam length and width are 100cm and 10cm respectively. crack is 05 cm in y-direction. I have attached data and...
  44. J

    Piezoelectric Actuator Cantilever Beam bending

    I do not have much knowledge in piezoelectric, but all the piezoelectric I've read up on seems to only achieve maximum displacement in measurement values of microns. Is it even possible for some piezoelectric actuator to bend a 10 meter long cantilever beam up to 1 meter at its maximum...
  45. D

    Calculating Bending Stress & Moment of Inertia for Tapered Cantilever Beam

    Hello all, I need to calculate the bending stress of a tapered cantilever beam. However, I would like to know how to calculate the moment of inertia. For a uniform shape beam, I know the Ix=(bh3)/12, but since h changes throughout the length of the beam how would inertia, I, be...
  46. N

    How Can Strain Be Calculated from Force Displacement Data in a Cantilever Beam?

    Hi everyone. I feel there should be a simple answer to this but I can't seem to find anything on this. So I have a simple cantilever beam, supported at one side and loaded at the free end. I have the force displacement data and can easily calculate the stress. However, for the strain I do...
  47. B

    Bending Moment of a Cantilever Beam

    This is a problem from Michael Lindeburg's FE Review Manual. It is in Chapter 20, Number 11 if you have the book. PROBLEM: There is a picture of a cantilever 2 m in length attached to a wall. There is a force applied at a 30 degree angle from the horizontal at the free end of the beam...
  48. K

    Cantilever beam with curved beam on the end.

    struggling to find info on this so figgured i'd as. For two beams attached to each other, one a straight catilever and the second a 90 degree bent beam attached to the end of the cantilever (shown in attached picture). To calculate the deflection of the beam at the load applied, given the...
  49. S

    Mechanical - Deflection and Slope, cantilever beam

    Hi guys, I have been a question to solve this week to do with deflections and slopes at the free end of a cantilever beam. I have calculated the deflection and slope for the point load and UDL, but I'm not sure whether to add them together or not?.. as they're both acting on the beam? A...