QUESTION 1(a) Sketch a bar element, a plane truss element, and a beam element. Label the axes, nodes andnodal degrees of freedom (dof). Identify the physical quantity of each dof.(b) Figure Q1(a) below shows a loaded cantilevered beam. The beam is made of a materialwith E = 200 GPa while the cross section of the beam is shown in Figure Q1(b).کسیس2 kN/m16 m10 KN(a)24 m8 kN40 kN-mFigure Q1200 mm(b)400 mm By using two (2) beam elements to model the beam, the nodal degrees of freedom are:NODE 2NODE 3-0.014-0.031-0.004-0.005Deflection (m)Rotation (radian)NODE 100At a section 3 m from the fixed end of the beam, calculate by using finite element method:(i) the deflection;(ii) the shear force;(iii) the bending moment;(iv) the maximum bending stress.

Answered: Image /qna-images/answer/f5e06e96-7c8b-47ba-bd2f-e1bfc3e2738d.jpg

QUESTION 1 (a) Sketch a bar element, a plane truss element, and a beam element. Label the axes, nodes and nodal degrees of freedom (dof). Identify the physical quantity of each dof. (b) Figure Q1(a) below shows a loaded cantilevered beam. The beam is made of a material with E = 200 GPa while the cross section of the beam is shown in Figure Q1(b).

QUESTION 1 (a) Sketch a bar element, a plane truss element, and a beam element. Label the axes, nodes and nodal degrees of freedom (dof). Identify the physical quantity of each dof. (b) Figure Q1(a) below shows a loaded cantilevered beam. The beam is made of a material with E = 200 GPa while the cross section of the beam is shown in Figure Q1(b).

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: The figure shows a cutaway view of an assembly in which a solid bronze [G= 6,500 ksi] rod (1) is…

A: From figure the rod and tube are connected at one end in series so, torque will be same. TBJ1 =…

Q: A cantilever beam model is often used to represent micro-electrical-mechanical systems (MEMS) (see…

Q: The failure stress of a homogeneous steel bar having a diameter of 10 mm is 250 MPa. Using a factor…

Q: A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another uniform…

Q: m in the following Figure. = members (including the beam) are el data: E, I, a E, A, a P

Q: The pin-connected structure shown in the figure consists of a rigid beam ABCD and two supporting…

Q: A bar made from aluminum (E = 72 GPa) has a diameter of 12 mm. When the bar is subjected to a…

Q: The frame shown is used to support high voltage cables. If b = 3 feet, a (alpha) = 30 ° and W = 200…

A: To determine the axial force in element HJ, we will need to apply the concept of static equilibrium.…

Q: A brass rod having a diameter of 4 in and a length of 40 ft is suspended vertically from one end. It…

A: Given, Diameter of rod = 4 in Length of rod = 40 ft Tensile load = 20 kips Modulus of elasticity =…

Q: The state of strain at a point in a rectangular block of material using an x-y coordinate system is…

Q: The beam cross section shown below has been proposed for a short pedestrian bridge. The cross…

Q: The figure shows a cutaway view of an assembly in which a solid bronze [G = 6,500 ksi] rod (1) is…

Q: Suppose we have a uniform beam that is 3.73 metres long has a flexural rigidity of 34301 Nm². N Find…

Q: Problem 5: A rigid bar of negligible weight is supported as shown in Figure. If W = 100 kN, a)…

A: W = 100 kN = 60 MPa

Q: The equation of deformation is derived to be y = x² - xL for a beam shown in the figure. L The…

A: Given data- The equation of deformation- y=x2-xL, To Find- The curvature of the beam at the…

Q: Two polymer bars are connected to a rigid plate at B, as shown. Bar (1) has a cross-sectional area…

Q: he pin-connected structure shown in the figure consists of a rigid beam ABCD and two supporting…

A: Given Data:Bronze alloyE=110 GpaA1=290mm2Aluminum alloyE=70 GpaA2=570mm2Assume…

Q: Problem 1: The figure presented here shows a horizontal beam of uniform density in static…

A: Given data,horizontal beam is givensupport provided at L/4 from left edgeTotal length=LF act at free…

Q: The tube is attached to a fixed plate at C, and both the rod and the tube are welded to a rigid end…

Q: The truss shown supports an automobile which has a mass of 2000 kg. Each member of the truss has…

Q: Pin G B (b) (a)

Q: A high-strength bolt that is passing through a steel plate is subjected to a tension force of P=4.6…

A: A) Given Data: Diameter of the bolt is db=12 mm. Diameter of the hole is D=14 mm. The tensile force…

Q: The beam shown below is made of an alloy of titanium that has a stress-strain diagram that can in…

Q: e the axial stress of the aluminum rod in the figure if the temperature of the steel rod is y 30…

A: The temperature of steel rod is increased by 30 degree.

Q: normal force in bar (1).

A: ### Calculation of Normal forces in bar 1 of given arrange of rigid beam ABCD ###

Q: The figure shows a cutaway view of an assembly in which a solid bronze [G= 6,500 ksi] rod (1) is…

Q: The geometry of the truss that you are to analyze is shown below in Figure 1. The load at joint B is…

A: Since value of theta is not given so reactions are find out in terms of theta values. So that we can…

Q: he thin-walled tube is used as a beam to support the uniformly distributed load of intensity wg. (a)…

A: Given:- Allowable bending stress = 100 MPa To find:- Value of wo Value of maximum shear stress

Q: The equation of deformation is derived to be y = x² - xL for a beam shown in the figure. The…

Q: 1. 30 kN 90 cm 555 cm - 27 kN Elastisite modülü 207 GPa olan ve silindir şeklindeki iki çubuktan 1…

Q: The intensity applied to beam AB is increased by a factor of 2. (i.e. your answer for the ntensity…

Q: A tapered circular rod of diameter varying from 30 mm to 20 mm is connected to another uniform…

Q: 2. As shown in the figure, a rigid beam with negligible mass is pinned at one end and supported by…

Q: -- A thin aluminum plate profile hown in the accompanying igure is subjected to an axial oad.…

A: Considering the section below:

Q: L M K 100 kg

Q: A nswers: a) ₁ = 0₂= (1) i i a C C b MPa MPa (2) D L2

Concept explainers

Members with compression and bending

Compression members are structural elements that carry compressive axial force. They are the vertical members of a building that support beams and their design, which is governed by buckling and strength. Columns are known as struct or compression members, which are subjected to compressive forces. These members provide stiffness to the building and avoid any imperfection regarding the transfer of axial load. For instance, webs in a truss, braces in a framed structure, tiers, and so on.

Question

By using two (2) beam elements to model the beam, the nodal degrees of freedom are:
NODE 2
NODE 3
-0.014
-0.031
-0.004
-0.005
Deflection (m)
Rotation (radian)
NODE 1
0
0
At a section 3 m from the fixed end of the beam, calculate by using finite element method:
(i) the deflection;
(ii) the shear force;
(iii) the bending moment;
(iv) the maximum bending stress.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduce the problem statement

VIEW

Step 2: State the characteristics of bar, truss and beam element

VIEW

Solution

VIEW

Step 3: Determine flexural rigidity of the beam

VIEW

Step 4: Formulate element stiffness matrices

VIEW

Step 5: Formulate global stiffness matrix

VIEW

Step 6: Formulate load vector matrix

VIEW

Step 7: Formulate displacement vector

VIEW

Step 8: Determine joint displacement

VIEW

Step 9: Determine support reactions

VIEW

Step 10: Compute maximum bending stress

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 11 steps with 29 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

Consider a rectangular cross-section beam having width b and height h that is taking bending load. The beam can be oriented in two different ways (shown in case a and b), and the corresponding neutral axes are shown as well. In which case, the beam will provide more resistance to bending (i.e., larger value of 1)? b Case (a) Neutral axis O I. Case (b) O II. Depends on other parameters III. Case (a) IV. Both cases will give the same value of I Case (b) Neutral axis
Q.23 A mild steel flat of width 120 mm and thickness 10 mm is bent into an arc of a circle of radius 10 m by applying a pure moment 'M". If E is 2 x 105 MPa, then the magnitude of pure moment will be □
Give the following problem a try. If you get stuck, here is one way to work it: Essential Solution Video. At a temperature of 44°F, a 0.06 in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [a = 15.3 × 10¯ 6/°F] and bar (2) is stainless steel [a = 8.4 x 10-6/°F]. The supports at A and C are rigid. Determine the lowest temperature at which the two bars contact each other. Assume L₁ = 30 in., L₂ = 63 in. (1) L₁ g B Answer: Final temperature = i L2 с °F.
Question @23
2. The steel bar with a cross-sectional area of 200 mm² carries the axial force at the position shown in the figure. If the modulus of elasticity of steel is 200 GPa, determine the total change in length of the bar. 12 kips 18 kips 10 kips 20 kips 3ft - 3ft-
QUESTION 2 a. Develop the general steps that are involved in finite element method procedures in terms of element, node and mesh. AE 100 AE L 1000 L 1 (2) Figure 2: Steel rod with two-bar elements A steel is subjected to compression as shown in Figure 2 above consists of different bar elements. Design:- b) Global stiffness matrix, K. c) Displacements at Node 2 and 3. d) Force value at Node 1 and 4. 10
The 16 x 22 x 25-mm rubber blocks shown are used in a double U shear mount to isolate the vibration of a machine from its supports. An applied load of P = 238 N causes the upper frame to be deflected downward by 4 mm. Determine the shear modulus G of the rubber blocks. Double U anti-vibration shear mount 25 Rubber block dimensions Shear deformation of blocks O 0.745 MPa O 0.883 MPa O 1.140 MPa
Please help me solve this, Thank you so much.
The figure shows a cutaway view of an assembly in which a solid bronze [G = 6,500 ksi] rod (1) is fitted inside of an aluminum alloy [G = 4,000 ksi] tube (2). The tube is attached to a fixed plate at C, and both the rod and the tube are welded to a rigid end plate at A. The rod diameter is d1 = 1.45 in. The outside diameter of the tube is D2 = 3.2 in. and its wall thickness is t2 = 0.140 in. Overall dimensions of the assembly are a = 42 in. and b = 6 in. The allowable shear stresses for the bronze and aluminum materials are 10700 psi and 8100 psi, respectively. Further, the rotation angle of end B must be limited to a magnitude of 5.9°. Based on these constraints, what is the maximum torque TB that can be applied at end B?
The figure shows a cutaway view of an assembly in which a solid bronze [G = 6,500 ksi] rod (1) is fitted inside of an aluminum alloy [G = 4,000 ksi] tube (2). The tube is attached to a fixed plate at C, and both the rod and the tube are welded to a rigid end plate at A. The rod diameter is d1 = 1.75 in. The outside diameter of the tube is D2 = 2.7 in. and its wall thickness is t2 = 0.130 in. Overall dimensions of the assembly are a = 38 in. and b = 13 in. The allowable shear stresses for the bronze and aluminum materials are 9400 psi and 7500 psi, respectively. Further, the rotation angle of end B must be limited to a magnitude of 5.1°. Based on these constraints, what is the maximum torque TB that can be applied at end B?
The pin-connected structure shown in the figure consists of a rigid beam ABCD and two supporting bars. Bar (1) is a bronze alloy [E = 91 GPa] with a cross-sectional area of A1 = 230 mm2. Bar (2) is an aluminum alloy [E = 70 GPa] with a cross-sectional area of A2 = 730 mm2. All bars are unstressed before the load P is applied; however, there is a 4-mm clearance in the pin connection at A. Assume L1 = 1660 mm, a = 950 mm, b = 550 mm, c = 410 mm, and L2 = 1230 mm. If a load of P = 176 kN is applied at B, determine (a) the normal stresses in both bars (1) and (2). (b) the downward deflection of point A on the rigid bar.
The figure shows a cutaway view of an assembly in which a solid bronze [G = 6,500 ksi] rod (1) is fitted inside of an aluminum alloy [G = 4,000 ksi] tube (2). The tube is attached to a fixed plate at C, and both the rod and the tube are welded to a rigid end plate at A. The rod diameter is d1 = 1.65 in. The outside diameter of the tube is D2 = 2.7 in. and its wall thickness is t2 = 0.130 in. Overall dimensions of the assembly are a = 49 in. and b = 11 in. The allowable shear stresses for the bronze and aluminum materials are 10500 psi and 7800 psi, respectively. Further, the rotation angle of end B must be limited to a magnitude of 5.6°. Based on these constraints, what is the maximum torque TB that can be applied at end B?