Example EXAMPLE 3.2 The structure consists of two bars. An axial load P = 200 kN is loaded as shown in Figure 3.10. Determine the following: (i) Element stiffness matrices (ii) Global stiffness matrix (iii) Global load vector (iv) Nodal displacements (v) Stress in each bar (vi) Reaction forces Steel $A_1 = 1000 \text{ mm}^2$ $E_1 = 200 \text{ GPa}$ 200 mm 100 mm Bronze $A_2 = 2000 \text{ mm}^2$ $E_2 = 83 \text{ GPa}$ Figure 3.10 A stepped bar.

          Example
EXAMPLE 3.2 The structure consists of two bars. An axial load P = 200 kN is loaded as shown
in Figure 3.10. Determine the following:
(i) Element stiffness matrices
(ii) Global stiffness matrix
(iii) Global load vector
(iv) Nodal displacements
(v) Stress in each bar
(vi) Reaction forces
Steel
$A_1 = 1000 \text{ mm}^2$
$E_1 = 200 \text{ GPa}$
200 mm
100 mm
Bronze
$A_2 = 2000 \text{ mm}^2$
$E_2 = 83 \text{ GPa}$
Figure 3.10 A stepped bar.

Example
EXAMPLE 3.2 The structure consists of two bars. An axial load P = 200 kN is loaded as shown
in Figure 3.10. Determine the following:
(i) Element stiffness matrices
(ii) Global stiffness matrix
(iii) Global load vector
(iv) Nodal displacements
(v) Stress in each bar
(vi) Reaction forces
Steel
A1 = 1000 mm^2
E1 = 200 GPa
200 mm
100 mm
Bronze
A2 = 2000 mm^2
E2 = 83 GPa
Figure 3.10 A stepped bar.

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University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Dwijendra Rao

Step 1

- Bar 1: Steel, length = 200 mm, cross-sectional area A₁ = 1000 mm², Young's modulus E₁ = 200 GPa - Bar 2: Bronze, length = 100 mm, cross-sectional area A₂ = 2000 mm², Young's modulus E₂ = 85 GPa Show more…

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Example 3.2: The Structure Consisting of Two Bars The structure consists of two bars. An axial load P = 200 kN is loaded as shown in Figure 3.10. Determine the following: i. Element stiffness matrices ii. Global stiffness matrix iii. Global load vector iv. Nodal displacements v. Stress in each bar vi. Reaction forces O 200 mm 100 mm Steel 1000 mm GP Bronze 2000 mm E83GP Figure 3.10: A Stepped Bar