Q1:Cosider the axially loaded nonprismatic member shown below. Using a quadratic isoparametric element (3 nodes), derive the stiffness matrix and the load vector due to self weight of the member. nodel node 3 node2 >2

Q1:Cosider the axially loaded nonprismatic member shown below. Using a quadratic isoparametric element (3 nodes), derive the stiffness matrix and the load vector due to self weight of the member. nodel node 3 node2 >2

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: Please explain each process as detail as possible. For the frame shown below, consider only the…

A: Static indeterminacy is known as the contrast of the entire number of unspecified and the entire…

Q: b) Determine the transformation matrix of all elements.

Q: For the truss shown below, use symmetry to determine the displacement of nodes and the stresses in…

A: Given- E=210 GPa, A=10-3 m2

Q: Determine the vertical displacement of joint C of the truss shown below using Castigliano's theorem.…

A: A truss is given with pin support at A and E.The truss also supports two point loads 24kN and 40kN…

Q: The uniform wire is bent into the shape shown and held by the frictionless pin at O. Determine the…

A: For the equilibrium to satisfy the centroid of the section should pass through O

Q: For the truss shown in Figure 3, members AC and BC have cross sectional area of 2 in.² while members…

Q: Use the method of joints to determine the force in each member of the truss. State whether each…

A: It is required to find forces in truss members.

Q: . For the three-node line element, in which node 2 is an interior node, shown below, obtain the…

A: SolutionTo solve for the shape functions and derive the element stiffness matrix for the three-node…

Q: stresses in each element. E=30E6 psi, Elemer ment 3 has Area = 20 in?, Use both software an 6 ft 2

Q: How many Gauss integration points (in one dimension, along s) will be needed to get the exact…

A: 1. Understanding the Four-Noded Bar ElementA four-noded bar element in one dimension has nodes at…

Q: Balancing the sums of the forces in the primed coordinate system yields two equations: 0x = 0x cos²…

A: Step 1: Step 2: Step 3: Step 4:

Q: For the truss shown below determine the vertical displacement at joint A using the method of virtual…

Q: Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial…

A: IAB=2000 cm4IBC=ICD=1000 cm4E=200 GPaLet IBC=ICD=I and…

Q: A simple plane truss is made of two identical bars (with E, A, and L), and loaded as shown in the…

Q: stone concrete slab that is used for an office. The slab is 200 mm thick. Sketch the loading that…

Q: QI. Using the force method of analysis, determine the forces in each member of the truss shown in Q.…

Q: The cross sectional area of each member of the truss shown in the figure is A = 500 mm^2 and E = 200…

A: Given- A truss carrying external horizontal load at C. Required- To calculate following by using…

Q: The natural frequencies of a cantilever beam are Wn(n=1,2...). How do you go about finding the…

Q: 1) Given the structure below, answer the following questions Determine the local stiff stiffness…

A: E= 10000 ksi A= 8 in2

Q: Problem 2-A concentrated couple, Mo = 600 Nm acts at the center of the simply Supported beam which…

Q: al member is

Q: d) Assemble the system stiffness matrix (movable DOFs only)

A: Find: System stiffness matrix (movable DOF only)

Q: A beam AB bears the force as follows, and the flexural stiffness of the beam section is constant EI:…

Q: Figure Q2 shows a 2-dimensional truss. The area of each member is equal to A. The modulus of…

A: Find: (a) Degree of freedom (b) Transformation matrix (c) Global stiffness matrix

Q: 2- The derivatives of the displacement components are related to the strain vector of the element as…

A: Structural design is a highly specialised field of structural engineering. It very well may be…

Concept explainers

Loads and Reactive Forces

Loads are the external influences that a beam experiences under its working conditions. For instance, a beam may be subjected to shear loads, twisting loads, bending moment, and axial loads during its working conditions. Engineers primarily deal with beams and trusses in the civil engineering domain. Due to the influence of loads, it is very crucial to determine the induced stresses and deformation values. These values give an insight into the critical area of the beam that needs to be worked upon to make it fail-safe.

Question

Civil Engineering
Finite Element Method
Q1:Cosider the axially loaded nonprismatic member shown below. Using a
quadratic isoparametric element (3 nodes), derive the stiffness matrix and
the load vector due to self weight of the member.
A1
nodel
IA
node 3
node2
A 21

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: To derive stiffness matrix

VIEW

Step 2: Load vector due to self weight:

VIEW

Step 3: Note:

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 13 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

Rod AB has a diameter d and fit snugly between the rigid supports at A and B when it is unloaded. The modulus of elasticity is E. Determine the support reaction at A and B if the rod is subjected to the linear distributed axial load. Po Pox p = B L.
2. Consider the vectors X₁ = (8,6) and x₂ =(4,-2) in R². (a) Determine the length of each vector. (b) Determine the length of X3 when X3 = X₁ + X2.
9 Consider the plane truss with load Pas shown in the figure. Let the horizontal and vertical reactions at the joint B be Hg and V, respectively and Vc be vertical reaction at the joint C. 2 exhoM S SLO 60° - II B A 60° D L 60° F 60° KLA G P с Which one of the following sets gives the correct values of VB, HB and V? (a) VB = 0; HB = 0; Vc = P (b) VB P/2; HB = 0; Vc = P/2 (c) VB = P/2; HB = P (sin60°); Vc = P/2 (d) VB = P; HB = P (cos(60°); Vc = 0 [2016
The truss in Figure 4 is loaded as shown. Both the nodes 1 and 5 are hinged supports. Take P = 27.8, L = 2.7, A = 0.0015 m2 and E=200 GPa. AE is constant for all the members. Use the stiffness method approach to solve parts (a) to (d) below. Write down your P and L values and answer parts a) to d) below. (a) Determine the stiffness matrices of the truss members 1, 4 and 5 in the global co-ordinate system with the origin at node 1. Use the member directions shown and clearly indicate the corresponding degrees of freedom numbers in the stiffness matrices. (b) Determine the stiffness matrices of elements 1 and 4 in the local co-ordinate system and then convert the respective local stiffness matrices to the global stiffness matrices. Show all calculations. Check the results with those obtained in part (a) above and comment. (c) Determine the load vector (Q) and displacement vector (D) and write the load-displacement relationship for the entire truss in the global co-ordinate…
Civil engineering Finite Elements questions Consider the 2-noded element shown in Fig. 1 that has nodes at x = −1 andx = +1.(a) Write the shape functions N1(x) and N2(x).(b) Show that the shape functions satisfy the Kronecker delta property, i.e., Ni(x) = 1 atnode i and zero at the other node(s).(c) Show that the shape functions satisfy the ”Rigid Body mode(s)” condition, i.e., N1(x)+N2(x) = 1.(d) Show that the shape functions satisfy the ”Constant Strain state(s)” condition, i.e.,N1(x)x1 + N2(x)x2 = x.
SOLVE STEP BY STEP IN DIGITAL FORMAT Determine by the method of nodes the forces at which all the members of the following truss work. A B 15 kN 4 m 3, 10 kN 2 m 4 m
Please do not copy any answers, they are incorrect.
HAND WRITTEN SOLUTION PLEASE!!! STRUCTURAL THEORY
Calculate the forces in all members using equilibrium of joint, ALso check weather the member is in tension or in compression. only HANDWRITTEN answer needed ( NOT TYPED)
Part F
Using Castigliano's Second Theorem. For the truss shown in the figure, Members AB, BC, CD, & AD have a cross-sectional area of 3 in2. Member BD have has a cross-sectional area of 4 in2. Modulus Elasticity for all members is 29 million pounds per square inch. If the value of P1 is 40 kips and P2 is 20 kips, determine the vertical deflection at B (in) and horizontal deflection at D (in). Put a negative sign if the reaction is downward or left direction.
Need neat and clean handwritten solution of both the parts with proper explanation..if you are not capable of doing than do not attempt as you will get downvote...