Consider the truss made of 2 bars with lengths 1 m, orientated in the structure shown in Figure 1. The two bars have the same cross-sectional areas A = 5-10-4 m² and modulus of elasticity E = 210¹¹ N/m². A force of F1,x = 10 kN is applied in the x-direction at node 1. fix fiy 90° fjs L ا fjv 2 1m 1 1m Figure 1: Truss assembly formed of two bars. Nodes and bars are numbered, with bars numbered with underlines. 3 a) Using the numbering system of nodes and bars shown in Figure 1, state the 2 local stiffness matrices for each bar and combine these into a global stiffness system for all nodal displacements of the truss. Use the matrix system given in Eq. 1 below relating the local displacements of a single bar to the local forces applied to its nodes. AE CS → Fax = 10KN Ľ 14₂ 2₂ CS -C² -CS S² -CS -S² -C² -CS C² CS Uj -CS -S²2 CS S² Here C = cos(0) and S = sin(0), where is the angle of orientation of the bar. (1) b) Apply the boundary conditions and specified forces to your global stiffness system of equations and solve for the displacements. c) What is the force required on node 1 for the displacement of the node 1 to be u₁ = 1·10-4 m and v₁ = 0m.

Consider the truss made of 2 bars with lengths 1 m, orientated in the structure shown in Figure 1. The two bars have the same cross-sectional areas A = 5-10-4 m² and modulus of elasticity E = 210¹¹ N/m². A force of F1,x = 10 kN is applied in the x-direction at node 1. fix fiy 90° fjs L ا fjv 2 1m 1 1m Figure 1: Truss assembly formed of two bars. Nodes and bars are numbered, with bars numbered with underlines. 3 a) Using the numbering system of nodes and bars shown in Figure 1, state the 2 local stiffness matrices for each bar and combine these into a global stiffness system for all nodal displacements of the truss. Use the matrix system given in Eq. 1 below relating the local displacements of a single bar to the local forces applied to its nodes. AE CS → Fax = 10KN Ľ 14₂ 2₂ CS -C² -CS S² -CS -S² -C² -CS C² CS Uj -CS -S²2 CS S² Here C = cos(0) and S = sin(0), where is the angle of orientation of the bar. (1) b) Apply the boundary conditions and specified forces to your global stiffness system of equations and solve for the displacements. c) What is the force required on node 1 for the displacement of the node 1 to be u₁ = 1·10-4 m and v₁ = 0m.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

Question

Consider the truss made of 2 bars with lengths 1 m, orientated in the structure shown in Figure 1. The
two bars have the same cross-sectional areas A = 5-104 m² and modulus of elasticity E= 210¹¹ N/m².
A force of F1,x = 10 kN is applied in the x-direction at node 1.
900
45°
2
=
AE
L
IN
2
1
1m
3
1m
→ F₁x = 10KN
Figure 1: Truss assembly formed of two bars. Nodes and bars are numbered, with bars numbered
with underlines.
y
a) Using the numbering system of nodes and bars shown in Figure 1, state the 2 local stiffness matrices
for each bar and combine these into a global stiffness system for all nodal displacements of the
truss. Use the matrix system given in Eq. 1 below relating the local displacements of a single bar
to the local forces applied to its nodes.
fix
fiy
fjr
fjv.
Here C = cos(0) and S = sin(0), where is the angle of orientation of the bar.
U₂
CS -C²-CS
S² -CS -S²
Vi
CS
-C² -CS C² CS Uj
-CS -S² CS S²
(1)
b) Apply the boundary conditions and specified forces to your global stiffness system of equations
and solve for the displacements.
c) What is the force required on node 1 for the displacement of the node 1 to be u₁ = 1.10-4 m and
V₁ = 0m.

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