1 Vukazich CE 160 Construction of Influence Lines for Beams [8] CE 160 Notes: Construction of Influence Lines for Beams Construct the influence line for the vertical reaction at the pin support for the beam (point A). Place unit dimensionless load at x = 0 (point A) and draw F.B.D. Use moment equilibrium to find support reaction at A Choose point B ! = 0 Counterclockwise moments about point B are positive 1 )( 12 − ! )(12 = 0 = (A y is positive so A y acts upward as assumed) 12 m A B C 3 m 12 m C 3 m 1 A x A y B y x +
12
Embed
CE 160 Notes: Construction of Influence Lines for Beams 160 constructing infl... · 1 Vukazich CE 160 Construction of Influence Lines for Beams [8] CE 160 Notes: Construction of Influence
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Counterclockwise moments about point D are positive
− 0.5 )( 6 𝑚 +𝑀! = 0
𝑴𝑫 = 𝟑 𝒎
Use force equilibrium to find VD
+↑ 𝐹! = 0
Upward forces positive
0.5 − 𝑉! = 0
𝑽𝑫 = 𝟎.𝟓
Place unit dimensionless load at x = 12 m (point B) and draw F.B.D. to find the support reactions
Note that from moment equilibrium and force equilibrium in the vertical and horizontal directions we find that Ay = 0; By = 1; and Ax = 0 Similar to the case when the unit load was at point A, no internal forces are developed in the beam so both VD and MD are zero.