Elongation in stepped bar. 2K subscribers Subscribe Question: 1.

Elongation in stepped bar Diagram Description: A stepped bar fixed at end D. Dimensions of the bar are shown in the figure below. 5 m long steel bar is having uniform diameter of 40 mm for a length of 1 m. Sep 13, 2022 · A stepped shaft of total length 2m is subjected to tensile load of 2000N as shown In the Fig. *Post-Tensioning Manual, fifth edition, Post-Tensioning Institute, Farmington Hills, MI, 1990, 406 pp. The bar has cross-sectional areas of A(1) and A(2) over the lengths `(1) and `(2), respectively. It involves: 1. below is made up of two different materials. 1 Thermal Stresses in Bars When the temperature of a circular bar of length l changes from an initial temperature T0 to its final temperature T1, the free thermal elongation λT of the bar is defined by Mar 12, 2024 · When 1. Model a tapered member of length L circular cross section as stepped shaft with several steps as shown in Figure P1. Tentukan jumlah pemanjangan sesuatu palang k APPENDIX D – POST-TENSIONING LOSSES AND ELONGATIONS The following appendix contains all the necessary information and formulas for calculating prestress losses and elongations for prestressed, post-tensioned structures. It helps in understanding how The modulus of elasticity of the stepped steel bar in the figure is E = 200 GPa, and there was a total elongation of 4 mm with the applied force P. A bar is subjected to an axial forces as shown in figure. 0050 in 5000 lb 6000 lb 12 in 8 in 8, in Figure 2 Loading scenario N2 2. Compare the result to the options provided. (E is the modulus of elasticity of the bar and A is its area of cross-section) This document discusses bars with cross sections that vary in steps or continuously. d=55mm,d=37mm,d=23mm. F=155kN. 2. 4. The material 1 has Young’s modulus = 2 × 105N/mm2, while that of material 2 is 1 × 10 5 N/mm2 . Assume that each bolt takes an equal part of the load. Question: 5. Calculate the elongation of the lear under its own weight. Strain: isotropic cross with Elongation: Homogeneous: Equilibrium: Homogeneous: Homogeneous, loaded Homogeneous, constant Material behavior: In body: straight, slender member with cross section that assumptions: that changes slowly along the length Total elongation of bar calculator uses Total Elongation = (Weight by Area*Length of Bar)/(2*Modulus of Elasticity Of Bar) to calculate the Total Elongation, Total elongation of bar formula is defined as a measure of the increase in length of a bar due to its own weight. F= 155kN. The forces are then split up and the m of the deformation of the individual sections. If however, the cross-sectional area is not uniform, the axial deformation can be determined by considering a differential length and applying integration. 2 mm. P10-11. Jun 4, 2021 · The percentage elongation or elongation after fracture in a tensile test is the remaining length variation (∆L-L) referred to as the initial measuring length (L) after a fracture. dBc 1 in CD 2 in AB 2 in Gap 0. Young's modulus is 2. For any query/ doubts ,you may ask in comment section or message me directly. Determine the magnitude of force P, such that the net deformation in the bar does not exceed 1 mm. What will be the diameter of a bar of uniform cross section, to have the same strain as that of the stepped bar? Take Young's modulus as 200 GPa. In this video, we’re going to explore a crucial concept in structural analysis—determining the change in length of a stepped bar subjected to varying Basic Answer The image shows a stepped bar that is loaded as described in the text. Check Elongation of Conical bar due to Self Weight example and step by step solution on how to calculate Elongation of Conical bar due to Self Weight. By measuring elongation, engineers and scientists can determine the extent to which a material stretches or deforms before it eventually breaks. the degree to which a material is supposed to be delivered, stretched, or compressed prior to rupture. FIGURE P10-11Question 1 (1 point) The value of the axial deformation of section "AB" is mm. In the 1D bar problem, we can calculate strain and stress in each element by, These quantities can be plotted Find an answer to your question A round stepped steel bar of diameters d and D with shoulder fillet r is subjected to axial tensile load P Find the ratio betwee… 11 Determine the total deformation between points A and D of a stepped steel bar subjected to the axial forces shown in Fig. 2-71): (Toa Derive the following formula YL2 for the elongation of the bar. A rectangular bar of length L has a slot in the central half of its length, as shown in Figure P5. Calculate the total deformation of the bar shown in figure. 1 (c). A stepped bar of diameters dAB-7/8 in, and dBc = 5/8 in. Show how the elongation converges to the exact value as the number of elements increase. 02 strain ε 0. Equations for the deformation in tapered bars involved integrating i remental deformations over the length of the bar. A1, E1, l1 A2, E2, l2 F2 F1 q1 q2 Strength Of Materials-Principle Of Superposition for bars of varying section. Home Assignment-4 - Elongation of Stepped Bars The document outlines a home assignment focused on problems related to bars with varying cross-sections. L1 =50 mm, L2 =25 mm, L3 = 17 mm. 3K subscribers Subscribed Nov 1, 2025 · A stepped bar is loaded as shown in Fig. In the next 0. The bar is composed of three segments with different cross-sectional areas and moduli of elasticity. 9K subscribers Subscribed #snsinstitutions #snsdesignthinkers #designthinking #aerospace #nehrukrish #gate2024 This video is about MECHANICAL ENGINEERING 1) stepped bar loadings and problems 2) Elongation due to self weight 3) Thermal stresses Detail telugu explanation. Divide the elongation by the original length of the bar and multiply by 100 to obtain the strain as a percentage. What is the change in diameter of the bar at section AA shown in the figure ? E= 2 x 10 N/mm2, density y = 8 x 10-5 N/mm² and Poisson's ratio m = 0. It provides examples of stepped bars, showing the stresses, strains, and extensions calculated for each section. To solve for the elongation, break the bar into lengths (segments) over which all the values (force, area and modulus) are constant. A solid aluminum stepped bar is loaded as shown. Length of each section is identical. It is a point among tensile strength and yield strength and is presented as a percentage of the original length. Calculate the stress in each part and total Elongation·E 2 105 N/mm2 · Area = 12 cm2 4-3000 N Area = 12 cm2-1000 N 500 mm 500 mm 750 mm Show transcribed image text Here’s the best way to solve it. Use Em10x10 psi for aluminum. It includes specific problems involving the calculation of extensions for bars made of different materials and varying diameters under tensile loads. Video 22 - Problem on calculation of Unknown Load 'P' & Total Elongation. Purpose: This calculator helps engineers determine how much a bar will stretch under load, which is crucial for structural design and material selection. https://www. Given F = 12500 lb; D = 1. [Diagram of a stepped bar with dimensions and forces applied] Views: 5,446 students Updated on: Nov 1, 2025 Jan 31, 2025 · Explanation: To find the elongation of the stepped bar due to its self weight, we will use the formula for elongation due to a uniform load. Question: For the stepped bar shown in the figure, it is requested to plot the diagrams of axial or normal force, normal stress and determine the absolute elongation of the bar, as well as the potential energy of deformation. com/channel/UCCqGTvGZgWw8mFX5KYTHCkw/sponsor#som #strengthofmaterial #education Elongation Calculation: Determine the elongation (ΔL) in each section using the formula: ΔL = ε * L, where L is the length of the section. Large end diameter and small end diameter of the tapering bar are 40 mm and 12. Determine the magnitude of force P such that the net deformation in the bar does not exceed 1mm. PTI Technical Note 1 The document is a finite element analysis question bank compiled by Ashok Kumar for RMK College of Engineering and Technology, covering various topics related to one-dimensional problems, shape functions, stiffness matrices, and dynamic analysis. Tensile Testing and Standards At a global level, technical committees governed by the International Organization for Standardization (ISO) develop product and testing standards for reinforcement bar products. Nov 4, 2025 · Solution For Find the stress, strain, and total elongation of a stepped bar subjected to an axial pull load of 40 kN. Step 2. 4K subscribers Subscribe Question: Problem 2: 30 points An axial load P is applied to a 150”-long continuous bar with the cross-sectional areas (A) shown in the figure below. Discretizing the bar into two elements based on the different cross sections. E for steel is 200extGP a, E for Aluminium is 70extGP a. 14 and develop a discrete element methodology to evaluate the free end elongation. The total elongation of the bar is calculated using force and stress equations for each region. Assume modulus of Elasticity of the material E=2 DERIVATION FOR UNIFORMLY TAPERING CIRCULAR AND RECTANGULAR SECTION BAR simple stress & strain HINDI 7. It also discusses how to calculate the total extension of a continuously tapering bar by considering incremental lengths and integrating over the entire length. 038 mm. Determine the elongation of the bar when the load is applied and the permanent elongation of the bar after unloaded σ (ksi) ay40 0. The bar has three segments with ELONGATION OF STEPPED BAR DUE TO SELF WEIGHT || STRENGTH OF MATERIALS CIVIL ACADEMIA 1. Tentukan jumlah pemanjangan sesuatu palang Determine the total elongation of the stepped steel bar under loads as shown in the Figure 1, if the modulus of elasticity, E=210GPa. E for steel is 200 GPa, E for Aluminum is 70 GPa. Figure description: Section 1 (Tapering Part Explanation Consider a rod of length L and uniform cross section of area A subjected to a centric P. Determine the change in its length. Assembling the element matrices into a global stiffness matrix. Location of nodes in a stepped bar problem exposed to different loads, replacement (displacement), element % elongation, element stresses, and end internal forces can be calculated in detail using the finite element method. At point A: 500 N acting to the Elongation Of Stepped Bar : Problem - 1 | Strength Of Material LEARN AND GROW 785K subscribers 6 Apr 27, 2019 · In this video we will discuss aboutPrinciple of superposition Bar of uniform section subjected to multiple loadingBar of varying section Bar of varying secti One Dimensional Tapered Bar Elements Problem Using Finite Element Analysis | 1D Problems in FEM Mahesh Gadwantikar 26. Diagram description: A bar composed of two sections. The bar has width b, thickness f, and elastic modulus E. 00 0. DERIVATION FOR UNIFORMLY TAPERING CIRCULAR AND RECTANGULAR SECTION BAR simple stress & strain HINDI 7. Show a graph of the elongation value versus number of The formula of Elongation Circular Tapered Bar is expressed as Elongation in Circular Tapered Bar = (4*Load*Length of Bar)/(pi*Diameter of Bigger End*Diameter of Smaller End*Elastic Modulus). Section BA: Length = 750 mm, Area = 6 cm². a) Calculate the total elongation ΔL of the bar. (In Hindi). Section CB: Length = 500 mm. Tentukan jumlah pemanjangan sesuatu palang APPENDIX D – POST-TENSIONING LOSSES AND ELONGATIONS The following appendix contains all the necessary information and formulas for calculating prestress losses and elongations for prestressed, post-tensioned structures. Elongation stands for a mechanical property of metal i. Mechanics of Solid Homework 3 Problem 2. If L = 400 mm, 6 = 45 mm, t = 8 mm, and E = 72 GPa, determine the overall elongation of the bar for an axial force of P = 18 kN. and made of an aluminum alloy is subjected to an axial force, di P, of 16 kips. The stepped steel bar shown in the sketch is loaded elastically by a tensile force F. 1 x 10⁵ N/mm². The modulus of elasticity for steel EST. 6/ A stepped bar ( E=200GPa ) is loaded as shown below. Question: Loading scenario #2: Modify the stepped bar loading and constraints to analyze the case shown in Figure 2 below. Find the deflection of point D (Elongation AD). The stress-strain relation for the material is given by the Ramberg-Osgood equation (Eq. Consider the modulus of elasticity 2. In addition to specifying properties, such as the minimum upper yield strength (Reh), Rm/Reh ratio, and elongation values for ribbed steel bar products, ISO product standards, such as ISO Jan 26, 2024 · Step-by-Step Guide: Calculating Elongation in Tensile Testing Calculating elongation in a tensile test is a crucial step in understanding the behavior of materials under stress. A 100 mm 70 mm -A + + ← 500 Total elongation of bar calculator uses Total Elongation = (Weight by Area*Length of Bar)/(2*Modulus of Elasticity Of Bar) to calculate the Total Elongation, Total elongation of bar formula is defined as a measure of the increase in length of a bar due to its own weight. Assume that the weight of the bar is small compared with the loading and can be neglected. In addition to specifying properties, such as the minimum upper yield strength (Reh), Rm/Reh ratio, and elongation values for ribbed steel bar products, ISO product standards, such as ISO Question: (b)A circular stepped bar ABC of length 40cm is subjected to an axial tensile load of 160KN as shown in figure below. 1 day ago · I can see: A 1. Find the total elongation in the bar. The strain energy in N-mm up to one decimal place in the bar due to the axial load is_______ 13. Aug 30, 2022 · Elongation of the bar problemsPrinciples of superpositionsTotal deformation of the circular Bar problemElongation of the stepped bar problemsMechanics of sol m of the deformation of the individual sections. Also included is an anchor set Aug 20, 2025 · View Strength_of_Materials_Exercise_01. This is the principle of superposition which may be stated as; "The total elongation in any stepped bar due to a load is the algebraic su of elongation Consider a bar made up of different lengths and having different cross-sections as shown in Fig. Aug 20, 2025 · Geometry of the solid is either constant or Kinematic to the axis before axis after deformation. 2 mm betw Question: 0-11 Determine the total deformation between points A and D of a stepped steel bar subjected to the axial forces shown in Fig. 2K subscribers Subscribe Question: 1. 97 ksi. This elongation occurs under the influence of gravitational forces and material properties, reflecting how materials deform Elongation of circular tapered barWith the help of this video student will be able to find elongation of tapered bar under external load*Important link *link The bars of varying sections, material properties, and dimensions, that are subjected to axial loads can be analyzed to determine their corresponding stress and strain values. E = 200 GPa. Elongation of tapered bar | Rectangular Cross-section| Derivation| Simple Stresses and Strains | L12This video is the twelfth lecture of Strength of Material The video lecture clarifies Calculation of Change in Length of Bar, Calculation of Unknown Load ' P', Calculation of Total Elongation of a Bar, Deflection of Stepped Bar, Deflection of Stepped Bar In this model, the main axis of the bar is discretized using linear, two-noded, 1D bar/truss finite elements having a uniform thickness within each element. NOTE: - For value: - Input the magnitude, and: - Use: - (+) for tension, elongation, please answer the . Question: 01: For the stepped rod shown, if the maximum allowable stress induced in the bar is not to exceed 150MPA and the maximum allowable elongation is not to exceed 2mm, find the maximum force P that can be applied. Example 4-4 The steel rod shown in Fig. 1. e. The analysis is perfo… Elongation Calculation: Determine the elongation (ΔL) in each section using the formula: ΔL = ε * L, where L is the length of the section. Find the extension of the bar under a pull of 30 kN if both the portions are 20 mm in thickness. The weight of the bar segment contributes to the elongation based on its length and cross-sectional area. d1 =55 mm, d2 =37 mm, d3 = 23 mm. 11-1 A bar AB of length L and weight density -y hangs vertically under its own weight (see figure). The elongation discrepancy problems greatly diminish with tendon lengths longer than 35 ft. If the stress in middle portion is limited to 150 N/mm², determine the diameter of the middle portion. Jan 6, 2022 · Example 2. 5extmm respectively. Large end diameter and small end diameter of the tapering bar are 40extmm and 12. 2mm. 083 to 2. Question 1 [23] Figure 1 shows a stepped bar with two steel rods, AB of 20mm diameter and CD of 15 mm, are connected by a copper bar of 35 mm diameter. This elongation occurs under the influence of gravitational forces and material properties, reflecting how materials deform The bars of varying sections, material properties, and dimensions, that are subjected to axial loads can be analyzed to determine their corresponding stress and strain values. b) Calculate the axial stresses in the cross sections 1,2 and 3 c) In addition to the force F, the bar is heated to 120∘C. A stepped bare with Circular crossection Dimension & supposted at top, hangs vertically under its own weight. Elongation/Force Relation: To solve for elongations, break up the bar into lengths over which all the values (force, area and modulus) are constant. 5-in diameter steel bar subjected to a tensile force of 30 kips, the stress in the bar if the bar in Problem 15 is 10 ft long, the elongation in the bar is 16. In this case a. It includes mathematical equations for calculating elongation and strain energy in members with varying cross-sections and provides examples with detailed solutions. 04 A stepped circular bar 150 mm long with diameters 20, 15 and 10 mm along length AB=40mm, BC=45mm and CD=65mm respectively is subjected to different forces as shown in the figure. Calculate the elongation of the bar under its own weight. 4–11 a has a diameter of 10 mm. The first section is 1extm long with a uniform May 17, 2025 · Explanation In this problem, we have a stepped bar subjected to axial loads. Question: Location of nodes in a stepped bar problem exposed to different loads replacement (displacement), element % elongation, element stresses and end internal forces calculate in detail using the finite element method? Question: Problem 2: 30 points An axial load P is applied to a 150”-long continuous bar with the cross-sectional areas (A) shown in the figure below. 2K subscribers Subscribe This document discusses the analysis of axially loaded structural members, focusing on the deformation of stepped and tapered rods under tension, and introduces the concept of strain energy. The document is part of educational Apr 27, 2019 · In this video we will discuss aboutPrinciple of superposition Bar of uniform section subjected to multiple loadingBar of varying section Bar of varying secti Nov 28, 2018 · To determine the total elongation of the bar having a uniform cross section problem, problem is based on principles of superposition, simple stresses and str One Dimensional Tapered Bar Elements Problem Using Finite Element Analysis | 1D Problems in FEM Mahesh Gadwantikar 26. 50 3000 lb 1500 lb 2000 lb -6. (10 points) What are the stresses from The formula of Elongation of Conical bar due to Self Weight is expressed as Elongation = (Specific Weight*Tapered Bar Length^2)/ (6*Young's Modulus). Check Elongation Circular Tapered Bar example and step by step solution on how to calculate Elongation Circular Tapered Bar. Compute the maximum tensile stress in the bar for the following dimensions: Help Videos: Walk through of Example BelowLinks to an external site. 5 m its diameter gradually reduces from 40 mm to 20 mm as shown in Fig. Yogendra Ram Meena 40. To use this formula, the load must be axial, the bar must have a uniform cross-sectional area, and the stress must not exceed the proportional limit. Deflection of Stepped Bar. Take E=200GPA. You’ll learn how to break down each section’s response to the axial loads and use fundamental equations to find the total elongation or compression of the bar. 5 mm respectively. 200 GPa and for copper is Ecu = 100 GPa P4 0,4 m B 0,6 m 0,2 m D P Figure 1: Stepped bar Determine the stresses in AB, BC, and CD if the total elongation of the 1. Calculate (i)the diameter (d) for the section BC if the stress in the member BC is 150N/mm². The diagram shows a stepped bar: - Large ends: 6 cm (60 mm) diameter, length 'a' each To use this formula, the load must be axial, the bar must have a uniform cross-sectional area, and the stress must not exceed the proportional limit. 9K subscribers Subscribed This document discusses the analysis of axially loaded structural members, focusing on the deformation of stepped and tapered rods under tension, and introduces the concept of strain energy. ? 100mm dia 14 500mm A A 1000 mm B 1000 mm 5 E= 2x10 MPa Y = 8x10S N mm u 0. Thus, the geometry is idealized as having a piecewise constant cross-section, as shown in Figure 2. Total Elongation: Sum the elongations of all sections to find the total elongation of the stepped steel bar. Elongation of bar given applied tensile load, area and length calculator uses Elongation = Axial Force*Original Length/ (Area of Cross-Section*Young's Modulus Bar) to calculate the Elongation, Elongation of bar given applied tensile load, area and length formula is defined as a measure of the increase in length of a material when subjected to a tensile force. Calculate stress in each part and total elongation. The elongation can be calculated by integrating the effects of the weight of each segment of the bar. Aug 24, 2025 · A stepped bar has three sections:500mm length with 20mm diameter, 400mm length with 25mm diameter, and 300mm length with 30mm diameter. Similarly, reduction of area, Z is the largest remaining cross-section change referred to the initial section after fracture of the test specimen. Included are example calculations for a simple-span structure stressed from one end and for a continuous structure stressed from one end. Exercise 1 — Axially Loaded Stepped Bar Problem A straight bar is built from two segments in series. 2:The stepped bar shown in Fig. 2 3 с Tomm * Please answer Question: A stepped bar is shown in fig. 4. Q. The dimensions of the bar are provided, including the length, width, and height. Solution Objective Compute the maximum tensile stress. Find also the length of the middle portion if the total elongation of the bar is to be 0. Thus, it is felt that meaningful conclusions and recommendations can be drawn from the study executed herein. The analysis is perfo… Question: 6/ A stepped bar ( E=200GPa ) is loaded as shown below. 00 -8. The dimensions are inches 1. Q1 (c). Watch this video till the end to know the value of these exams and tips to crack the GATE and ESE exam. It includes a series of questions addressing concepts such as node numbering, properties of shape functions, and element formulations, focusing on I can see: A round bar with stepped portion is subjected to the forces as shown in fig. 2. The modulus of elasticity of steel is E=210GPa. 200 GPa and for copper is Ecu = 100 GPa P4 0,4 m B 0,6 m 0,2 m D P Figure 1: Stepped bar Determine the stresses in AB, BC, and CD if the total elongation of the Jan 8, 2025 · Consider the stepped bar made with a linear elastic material and subjected to an axial load of 1 kN as shown in the figure. The initial portion of the stress-strain curve is shown in the figure. Video 21 - Problem on Maximum Axil Pull and Total Elongation. These calculations are performed in this step. 3. 0 m m (a) Does enlarging the bar in the middle region make it stronger than the prismatic bar? Demonstrate The slot has width 6/3. The total elongation of the bar is 200 GPa. Calculate elongation of bar due to its own weight and load (P) applied Note: the weight of the bar itself produces a varying internal axial force which is zero at the lower end and is maximum at the upper end Find the stresses induced in the axially loaded stepped bar shown in Figure 1. 0mm 2. Principle of Superposition for Elongation of a Composite Bar: Fig 4 at some intermediate sections along its length. 00 - 12. The video lecture clarifies Calculation of Change in Length of Bar, Calculation of Unknown Load ' P', Calculation of Total Elongation of a Bar, Deflection of Stepped Bar, Deflection of Stepped Bar In this model, the main axis of the bar is discretized using linear, two-noded, 1D bar/truss finite elements having a uniform thickness within each element. 10 ^ 5 MPa. (2marks) (ii)length of AB,if the total elongation (AL) of the bar is 0. The modulus of elasticity of steel is E =210GPa. The normal stress s is a maximum when θ = 0° a ion d in tapered and stepped bars were described. The Young's modulus (E) is given as 200 GPa. Chapter 3: Tapered Bar Keywords: 1D elasticity, 2D elasticity, plane stress, model symmetry, convergence Modeling Procedures: ruled surface, convert Nov 16, 2023 · To calculate the minimal longitudinal strain of the stepped bar, calculate the strain for each element and the elongation of the entire bar using Young's modulus. Jun 23, 2025 · The bar shown in fig. The stress-strain relation of the material used to make this bar obtained during a tension test can be expressed as follows 4 = 16000 + G85) where o is the normal stress in ksi. Segments 1 and 2 have cross sectional area of 100 mm 2 and 60 mm 2, Young’s modulus of 2 × 10 5 MPa and 3 × 10 5 MPa and length of 400 mm and 900 mm respectively. L=50mm,L=25mm,L=17mm. 50 in; d = 0. This document presents the finite element analysis of a stepped bar under tensile loading. What is the change in diameter of the bar at section A-A shown in the figure? T 1000 mm 1000 mm TE 500 mm A 100 mm dia 70 mm dia E = 2 x 105 N/mm², density y = 8 x 10-5 N/mm³ A prismatic bar with a diameter d0 = 20 d 0 = 20 mm m m is being compared with a stepp ed bar of the same diameter (d1 = 20mm) (d 1 = 20 m m) that is enlarged in the middle region to a diameter d2 = 25mm d 2 = 25 m m (see figure). 7/ What would be the appropriate diameter of the bolts in the illustration below knowing that the maximum permissible shear stress is 140MPa. 75 in; r = 0. 7/ What would be the appropriate diameter of the bolts in the illustration below knowing that the maximum permissible shear stress is 140MPa. Use LAB = 18in; LBC = 13in; dAB = 7/8 in; dcp = 5/8 in; P = 15 kips; E = 10 (10 psi (a) Determine the elongation of the bar Jan 8, 2025 · Consider the stepped bar made with a linear elastic material and subjected to an axial load of 1 kN as shown in the figure. This is a continuation video, first Dec 2, 2024 · You can JOIN US by sign up by clicking on this link. Given E = 200 GN/m². pdf from CEE 6551 at Georgia Institute Of Technology. Determine the total elongation of the stepped steel bar under loads as shown in the Figure 1, if the modulus of elasticity , E=210. (You do not need to create the wall beyond the gap to complete this analysis). Area of cross section A1,A2,A3&A4 are 400mm^2,200mm^2,100mm^2 and Model a tapered member of length L circular cross section as stepped shaft with several steps as shown in Figure P1. It is fixed to the wall at A , and before it is loaded, there is a gap of 0. The initial portion of the stress-strain curve is given below. The strain energy in N-mm up to one decimal place in the bar due to the axial load is_______ The modulus of elasticity for steel EST. The document is part of educational A stepped bar is loaded as shown in the figure. Take modulus of elasticity, The stepped steel bar shown in the sketch is loaded elastically by a tensile force F. Axially-loaded Members Structural components subjected only to tension or compression: coil springs, solid bars with straight longitudinal axes, cables, etc. We will use the formula for elongation due to axial load: ΔL= AEP L where: ΔL = change in length P = axial load L = original length s τ both vary with the angle of the section cut. The bar consists of two sections with different diameters and lengths. The stepped bar shown in the above figure is subjected to an axial tensile force of 12500 lb. Helpful Ask follow-up Video 20 - Problem No. The slot has width 6/3. Strain: isotropic cross with Elongation: Homogeneous: Equilibrium: Homogeneous: Homogeneous, loaded Homogeneous, constant Material behavior: In body: straight, slender member with cross section that assumptions: that changes slowly along the length A stepped bar with circular cross-section and supported at top, hangs vertically under its own weight. Explore the fascinating concept of stress and elongation in a rotating bar in this detailed Solid Mechanics lecture! This video dives deep into the effects o Jul 21, 2025 · This problem involves a stepped bar fixed at both ends, meaning the total net deformation of the entire bar from end to end is zero. The analysis for step bars involved sum The drawing shown below is a representation of a re-designed stepped bar component utilised in a field cultivator employed in the farming industry to prepare soil for planting. But we often need to calculate other physical quantities such as strain and stress in the element and visualize them in the contour plots or graphs. Elongation of Stepped Bar is explained in this video. Dimensions of the bar are as shown in the figure below. find the change in diameter of bar at Section shown figure ilmu LALA of A-A in the . The bar has two sections: Section DC: Length = 500 mm, Area = 12 cm². The radius of the fillets in the stepped bar is 2. Deriving the element stiffness matrices for each element. The stepped bar consists of a 22 mm square section bar (AB) of length 50 mm; a 13 mm diameter bar (BC), length 55 mm and a 6 mm diameter bar (CD), length 40 mm. An example problem is given to find Apr 24, 2020 · With the help of this video student will be able to find elongation of rectangular tapered bar*Important link *strain energy when load applied suddenlyhttps: A stepped bar with circular cross-section and supported at top, hangs vertically under its own weight. 00 6/ A stepped bar ( E=200GPa ) is loaded as shown below. the elongation is N(x) dx = d CCCC A(x) the elongation of the entire bar is obtained by integrating Jan 25, 2025 · In case of a stepped bar of a material subjected to an axial load, the total elongation is proportional to __________ This question was previously asked in SNS COURSEWARE - New This is a online courseware website for sns college students through this website student can access their materials The drawing shown below is a representation of a re-designed stepped bar component utilised in a field cultivator employed in the farming industry to prepare soil for planting. The change in length of AB is: Since AB is in compression, it shortens: Da<0. Applying the boundary conditions of zero displacement at one end and known force Jan 5, 2025 · A round bar with stepped portion is subjected to the forces as shown in Fig. of the bar is as shown below. youtube. We need to determine the load P and the change in length of the bar. If the bar is subjected to a 60KN axial load, calculate the total elongation (E=200Gpa) IES/Gate - ELONGATION OF STEPPED BAR - Fixed at one end and different loads acting on it chalkandboard 37. Forces applied: At point C: 1500 N acting to the left. 11 (a) is subjected to a tensile load of 160 kN. The force P is determined to be 130 kN for static force equilibrium. The top length of the bar AB, has length a, area A 1, modulus E 1, and carries force P a = -W (compression). If the resulting axial stress: Definition: Elongation refers to the change in length of a material when subjected to an axial tensile force. 2K subscribers Subscribe A stepped bar with diameters dAB and dcp made of an aluminum alloy is subjected to an axial force Pas shown below. Welcome to this tutorial on stepped bar. Question 1 [23] Figure 1 shows a stepped bar with two steel rods, AB of 20mm diameter and CD of 15 Post-Processing The nodal DOF are only obtained by solving the global system of equations. GPa. 5 tech Manoj Engineering Vines 10. a) Determine the axial elongation (in Axial Loading (Case 2) on Stepped bar (Bars in series)- Maximum stress developed in bar & deformation at free end & draw Axial Loading diagram Please rate , review , recommend and share . Determine the elongation of this bar when subjected to an axial tensile load of 160 kN. This is the principle of superposition which may be stated as; "The total elongation in any stepped bar due to a load is the algebraic su May 18, 2009 · Elongation/Force Relationship. The image also includes several options for the diameter of the bar, ranging from 2. 9 Elongation of tapering bars of circular cross section Consider a circular bar uniformly tapered from diameter d1 at one end and gradually increasing to diameter d2 at the other end over an axial length L as shown in the figure below. 4 For such a bar, the following conditions apply: Figure 8 Axially loaded bar as a spring-mass system Now, we can also analyze a stepped bar (a bar with two different cross-section areas) under two concentrated forces F1 and F2 as shown in Figure 9. rgr xqa zqa wpihb hieenzx kphx sfims wwwyyp ipwwign jrosxm fhz zpiuuc cioarrl phbe khson