The beam shown in Figure 1 supports a distributed live load of 1.5 kN/m, and a single concentrated load of 10 kN. In addition, the dead load is 2.0 kN/m. D is a fixed support, B is a roller support and joint C is a hinge. Determine the followings: (a) the key points for the influence lines for the vertical reactions at B (By) and D (Dy) and moment at D (MD). Fill up Table 1 with your calculated values. (b) sketch the influence lines for the vertical reactions at B (By) and D (Dy) and moment at D (MD). the maximum vertical reaction at B (By) for the given loads. the maximum negative moment at D (MD) for the given loads. (c) (d)

The beam shown in Figure 1 supports a distributed live load of 1.5 kN/m, and a single concentrated load of 10 kN. In addition, the dead load is 2.0 kN/m. D is a fixed support, B is a roller support and joint C is a hinge. Determine the followings: (a) the key points for the influence lines for the vertical reactions at B (By) and D (Dy) and moment at D (MD). Fill up Table 1 with your calculated values. (b) sketch the influence lines for the vertical reactions at B (By) and D (Dy) and moment at D (MD). the maximum vertical reaction at B (By) for the given loads. the maximum negative moment at D (MD) for the given loads. (c) (d)

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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Concept explainers

Influence Lines

The graphs that show the variation of a function at a specific point on a beam or truss due to a unit load placed at any point along the structure are known as influence lines in engineering. Some common functions that are studied with influence lines are shear, moment, and deflection. In designing beams and trusses, it is important to use influence lines in structures where loads would move along their span such as bridges, crane rails, conveyor belts, floor girders, etc. The influence lines help to study where a load will create the maximum effect for any of the functions.

Question

The beam shown in Figure 1 supports a distributed live load of 1.5 kN/m, and a single
concentrated load of 10 kN. In addition, the dead load is 2.0 kN/m. D is a fixed support, B is
a roller support and joint C is a hinge. Determine the followings:
(a)
the key points for the influence lines for the vertical reactions at B (By) and D
(Dy) and moment at D (MD). Fill up Table 1 with your calculated values.
(b)
sketch the influence lines for the vertical reactions at B (By) and D (Dy) and
moment at D (MD).
(c) the maximum vertical reaction at B (By) for the given loads.
(d)
the maximum negative moment at D (MD) for the given loads.

Table 1:
A
Key Points
A
B
C
D
2m
B
X (m)
0
2
6
8
4m
Figure 1
By
C
Dy
2m
D
MD

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