5. Influence Lines

5.3 Suggested Problems

Problem 5.3-01

Sketch influence lines for the following effects:

1. Moment at $a$.
2. Moment at $b$.
3. Shear at $b$.
4. Shear at $c$.
5. Shear just to the left of $d$.
6. Shear just to the right of $d$.
7. Moment at d.
8. Shear at $e$.
9. Shear just to the left of $f$.
10. Shear just to the right of $f$.
11. Moment at $f$.

The structure is subjected to a uniform live load of 20kN/m and a concentrated live load of 60kN (acting simultaneously). Determine the range of each effect for this loading condition. Show the correwsponding position of the loads, for each.

(Partial-Solution - influence lines)

(Partial-Solution - effect of live loads)

Problem 5.3-02

Sketch influence lines for the following effects:

1. Vertical reaction at $a$.
2. Moment at $a$.
3. Shear at $b$.
4. Moment at $b$.
5. Moment at $c$.
6. Vertical reaction at $d$.
7. Shear just to the left of $d$.
8. Shear just to the right of $d$.
9. Moment at $d$.

(Partial-Solution)

Problem 5.3-03

In the above frame, loads are applied vertically to the horizontal member $bcdef$. Sketch influence lines for the following effects.

1. Vertical reaction at $a$.
2. Horizontal reaction at $a$.
3. Moment $M_{ba}$ at the top of the column $ab$.

(Partial-Solution)

Problem 5.3-04

In the above frame, loads are applied vertically to the horizontal member $efg$. Sketch influence lines for the following effects.

1. Vertical reaction at $a$.
2. Moment at $c$.
3. Moment at $b$.
4. Vertical reaction at $e$.

(Partial-Solution)

Problem 5.3-05

In the above structure, vertical loads are applied to the stringers, which in turn are simply supported by the girder. Draw influence lines for the following effects:

1. Vertical reaction on the girder, at $a$.
2. Moment in the girder at point $b$ (midway between the supports).
3. Shear in girder just to the left of the support at $c$.
4. Moment in the girder over the support at $c$.
5. Moment in the girder at point $d$ (at the centre of the span).
6. Shear in the girder just to the right of the support at $c$.
7. Vertical reaction on the girder at $c$.

(Partial-Solution)