10.3. The two-span beam with equal spans I is subjected to force P as shown in Fig. 10.14a. The beam is divided into ten equal portions; the number of joints is presented in Fig. 10.1le. Find the reaction at the middle support B. Solve this problem by three different ways (a) Use the influence lines for Mg and Qk: (b) use the influence lines for primary unknown of the displacement method; (c) use the influence lines for primary unknown of the force method. 0.4/ RA 0.4/ 0.6 R 0.096P b Influence line for M P=1 LoadP=1 0.0384 PI 0.4/ in the left span 0.096P M depends of position P the left or right at k 0.41 0.6/ Load P=1 in the right span 8. M = 0 for any position Pt ul=0.41 ul=0.6! R RC 8. 0.6/ X;{1+0.6P Fig. 10.14 (a) Design diagram of the beam and calculation of reaction at support B using the influ- ence line for internal forces at section k. (b) Calculation of reaction at support B using the influence line Z, of the displacement method. (e) Calculation of reaction at support B using the influence line X, of the force method 902 0.0336 19180'0 8001'0 0.0192

10.3. The two-span beam with equal spans I is subjected to force P as shown in Fig. 10.14a. The beam is divided into ten equal portions; the number of joints is presented in Fig. 10.1le. Find the reaction at the middle support B. Solve this problem by three different ways (a) Use the influence lines for Mg and Qk: (b) use the influence lines for primary unknown of the displacement method; (c) use the influence lines for primary unknown of the force method. 0.4/ RA 0.4/ 0.6 R 0.096P b Influence line for M P=1 LoadP=1 0.0384 PI 0.4/ in the left span 0.096P M depends of position P the left or right at k 0.41 0.6/ Load P=1 in the right span 8. M = 0 for any position Pt ul=0.41 ul=0.6! R RC 8. 0.6/ X;{1+0.6P Fig. 10.14 (a) Design diagram of the beam and calculation of reaction at support B using the influ- ence line for internal forces at section k. (b) Calculation of reaction at support B using the influence line Z, of the displacement method. (e) Calculation of reaction at support B using the influence line X, of the force method 902 0.0336 19180'0 8001'0 0.0192

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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