Situation 3. The trame is loaded as illustrated in Figure 3 and is hinged at point C. Sketch the shear, bendingmoment, and axial diagrams. Also draw the qualitative deflected shape as an overlay on the original frame.15 kN/m2m50 kN80 AN2 m4 m3 m3mFigure 3

Data given: Asked: Sketch shear, Bending moment and Axial force diagram

Answered: Situation 3. The trame is loaded as…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

Situation 3. The trame is loaded as illustrated in Figure 3 and is hinged at point C. Sketch the shear, bending
moment, and axial diagrams. Also draw the qualitative deflected shape as an overlay on the original frame.
15 kN/m
2m
50 kN
80 AN
2 m
4 m
3 m
3m
Figure 3

Expert Solution

Step 1 Interpretation of data

Data given:

Asked:

Sketch shear, Bending moment and Axial force diagram

Step 2 Primary calculations

Consider following free body diagram for given frame:

The angle $θ$ can be obtained by,

$θ = \tan^{- 1} (\frac{2}{6}) = 18.44 °$

Take summation of moment at C = 0,

$∴ (V_{E} \times 3) - (15 \times \frac{6.325}{2} \times \frac{6.325}{4}) - (50 \times 1) = 0 ∴ V_{E} = 41.67 kN$

Take $\sum_{}^{} V = 0$ ,

$∴ V_{A} + V_{E} = (15 \times 6.325) ∴ V_{A} + V_{E} = 94.875 kN ∴ V_{A} = 94.875 - 41.67 = 53.2 kN$

Finally, consider $\sum_{}^{} H = 0$ ,

$H_{A} = 80 - 50 = 30 kN$

In order to find Moment at A. let's again consider summation of moment at point C from left hand side,

$- M_{A} + (53.2 \times 3) + (30 \times 5) - (80 \times 1) - (15 \times \frac{6.325}{2} \times \frac{6.325}{4}) = 0 ∴ M_{A} = 154.6 lN - m$

Step 3 Calculations for axial force diagram

$In member AB, Axial force = 53.2 kN In member DE, Axial force = 41.67 kN In member BD Axial force = [(80 - 30) \times \sin 18.44 °] + (53.2 \times \cos 18.44 °) = 66.28 kN$

Step by step

Solved in 5 steps with 5 images

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions