Solution:

Influence Line Diagrams:

An influence line diagram is a graphical representation of how a particular response function at a specific point on a structure is influenced by a unit load applied at any point along the structure. The influence line diagram can be used to determine the maximum or minimum value of any response function for a given structure.

In this problem, we need to determine the influence line diagrams for the bending moment and shear force at a section 10m from the left support of the simply supported beam.

Bending Moment Influence Line Diagram:

To determine the bending moment influence line diagram at a section 10m from the left support, we need to place a unit load at different locations along the beam and determine the corresponding bending moment at the section of interest.

Let us place a unit load at a distance x from the left support. The bending moment at a section 10m from the left support due to this unit load can be determined using the formula:

M = wx(25-x)/2

where w is the load intensity, and x is the distance from the left support.

The bending moment influence line diagram can be obtained by plotting the bending moments at the section of interest due to the unit loads placed at different locations along the beam. The resulting influence line diagram is shown below:



Shear Force Influence Line Diagram:

To determine the shear force influence line diagram at a section 10m from the left support, we need to place a unit load at different locations along the beam and determine the corresponding shear force at the section of interest.

Let us place a unit load at a distance x from the left support. The shear force at a section 10m from the left support due to this unit load can be determined using the formula:

V = w(25-x)

where w is the load intensity, and x is the distance from the left support.

The shear force influence line diagram can be obtained by plotting the shear forces at the section of interest due to the unit loads placed at different locations along the beam. The resulting influence line diagram is shown below:



Maximum Bending Moment:

The maximum bending moment at a section 10m from the left support can be determined by multiplying the maximum ordinate on the bending moment influence line diagram by the magnitude of the load. From the influence line diagram, the maximum ordinate occurs when the unit load is placed at a distance of 15m from the left support. The corresponding bending moment is:

Mmax = wx(25-x)/2 = 10(15)(25-15)/2 = 750 kNm

Therefore, the maximum bending moment at a section 10m from the left support is 750 kNm.

Absolute Maximum Shear Force and Bending Moment:

To determine the absolute maximum shear force and bending moment in the beam, we need to consider the effect of all the loads on the structure.

The shear force and bending moment diagrams for the simply supported beam with the given loads are shown below:


From the shear force diagram, the absolute maximum shear force occurs when the 120 kN load is at the section of interest. The corresponding shear force is:

Vmax = 80 + 160 + 160 + 120 = 520 kN

From the bending moment diagram, the absolute maximum bending moment occurs at the mid-span of the