Slope-Deflection.pdf - Concept of fixed end moments Obtained using unit load method 1 Derivation of the Slope-Deflection Equation Figure 12.5 Fixed-end

# Slope-Deflection.pdf - Concept of fixed end moments...

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1 Concept of fixed end moments Obtained using unit load method

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2 Derivation of the Slope-Deflection Equation Figure 12.5 Fixed-end moments
3 Derivation of the Slope-Deflection Equation Figure 12.5 Fixed-end moments (continued)

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4 Derivation of the Slope-Deflection Equation Figure 12.5 Fixed-end moments (continued)
5 Derivation of the Slope-Deflection Equation Figure 12.5 Fixed-end moments (continued)

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6 Derivation of the Slope-Deflection Equation Figure 12.2 Continuous beam whose supports settle under load
7 §12.3 Derivation of the Slope-Deflection Equation Deformations of member AB plotted to an exaggerated vertical scale

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8 Derivation of the Slope-Deflection Equation Figure 12.4
9 Illustration of the Slope-Deflection Method Figure 12.1 Continuous beam with applied loads (deflected shape shown by dashed line)

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10 §12.3 Derivation of the Slope-Deflection Equation Deformations of member AB plotted to an exaggerated vertical scale
11 §12.3 Derivation of the Slope-Deflection Equation Deformations of member AB plotted to an exaggerated vertical scale N F x

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12 Illustration of the Slope-Deflection Method Free bodies of joints and beams (sign convention: Clockwise moment on the end of a member is positive )
13 Analysis of Structures by the Slope- Deflection Method Figure 12.7 All joints restrained against displacement; all chord rotations ψ equal zero Due to symmetry of structure and loading, joints free to rotate but not translate; chord rotations equal zero

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14 Analysis of Structures by the Slope- Deflection Method Figure 12.7 (continued) Unbraced frames with chord rotations
15 Example 12.2 Using the slope-deflection method, determine the member end moments in the indeterminate beam shown in Figure 12.8 a . The beam, which behaves elastically, carries a concentrated load at midspan. After the end moments are determined, draw the shear and moment curves. If I = 240 in 4 and E = 30,000 kips/in 2 , compute the magnitude of the slope at joint B .

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16 Example 12.2 Solution Since joint A is fixed against rotation, θ A = 0; therefore, the only unknown displacement is θ B. Using the slope- deflection equation The member end moments are: To determine θ B , write the equation of moment equilibrium at joint B
17 Example 12.2 Solution (continued) Substituting the value of M BA and solving for θ B give where the minus sign indicates both that the B end of member AB and joint B rotate in the counterclockwise direction To determine the member end moments,

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18 Example 12.2 Solution (continued) Free body used to compute end shears To complete the analysis, apply the equations of statics to a free body of member AB To evaluate θ B , express all variables in units of inches and kips.
19 Example 12.2 Solution (continued) Shear and moment curves Expressing θ B in degrees

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20 Example 12.3 Using the slope-deflection method, determine the member end moments in the braced frame shown in Figure 12.9 a . Also compute the reactions at support D , and draw the shear and moment curves for members AB and BD .
• Fall '19
• chandiramani

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