# Combined Bending and Direct Stress Tutorial Questions

These tutorial questions consider a variety of different problems that are related to the calculation of combined bending stress and direct stress present in members and structures under different loading conditions. They get progressively more complex and are designed to be worked through sequentially. When selected, the variables present for each tutorial question is randomly generated giving an infinite number of possible questions to be attempted. Additionally there are randomly generated worked examples and printed tutorial sheets to assist with the tutorial questions.

Each tutorial is selected by selecting the appropriate question number below. Notes:

• The analysis associated with these tutorial questions will round all your input values as follows:
• Forces, e.g. vertical and horizontal reactions (kN) - 3 decimal place.
• Dimensions (m) - 3 decimal places.
• Angles (°) - 3 decimal place.
• Numeric answers are required in all the fields. If you calculate a force as being zero, enter zero (0) in the appropriate field.
• You are only able to print the current question as a tutorial question if you have not submitted your answers.
• Once a tutorial question has been printed, you will not be able to submit your answers, or see the solution to that particular question.

Notation:

• ∅ - Diameter of an object (mm).
• I - Second moment of area of cross section (mm4).
• ρ - Density of a material (N/mm²).
• σ - Compressive or tensile stress within a material (N/mm²).
• e - Eccentricity of a load (mm). A compressive force is acting at an eccentricity along the Z-Z and Y-Y axis of the section that is shown in plan view. For the given case calculate the following:

• The stress at points A, B, C and D.

### Solution

#### Stress

Calculate the stress at the locations marked A, B, C, and D.

σA =
N/mm2
σB =
N/mm2
σC =
N/mm2
σD =
N/mm2 A concrete wall is to be used to retain a mass of soil. The soil is exerting a horizontal pressure onto the wall acting over it's full height. Taking a unit length for the given case calculate the following:

• The minimum and maximum stress at the base of the wall.

Draw the stress diagram for the stress distribution of the base of the wall.

### Solution

#### Stress

Calculate the minimum and maximum stress at the base of the wall.

σMin =
N/mm2
σMax =
N/mm2 A universal column section is subject to multiple forces that are acting at eccentricities along the Z-Z and Y-Y axis. For the given case calculate the following:

• The second moment of area about the Z-Z and Y-Y axes.
• The stress at points A, B, C and D.

### Solution

#### Second moment of area

Calculate the second moment of area about both axis.

Izz =
mm4
Iyy =
mm4

#### Stress

Calculate the stress at the locations marked A, B, C and D.

σA =
N/mm2
σB =
N/mm2
σC =
N/mm2
σD =
N/mm2 A bracket has been formed from two steel T sections that have been welded together and supported as shown. This bracket is responsible for carrying an inclined point load. A cross-section of the bracket has been taken at the point marked A-B displaying the sections geometrical properties. For the given case calculate the following:

• The second moment of area about the Z and Y Axes.
• The stress that is present at point A and B.

Sketch the stress diagram indicating the values of stress at point A and B.

### Solution

#### Second moment of area

Calculate the second moment of area about both axis, where Izz is the primary axis and Iyy is the secondary axis.

Izz =
mm4
Iyy =
mm4

#### Stress

Calculate the stress at the locations marked A, B, C and D.

σA =
N/mm2
σB =
N/mm2 A street light is located on an embankment resulting in an inclination of the structure. The weight of the street light can be resolved into two forces acting at a distance from the base of the pole. For the given case calculate the following:

• The second moment of area of the pole.
• The minimum and maximum stress at the base of the pole.

Sketch the stress diagram indicating the values of minimum and maximum stress.

### Solution

#### Second moment of area

Calculate the second moment of area of the pole.

I =
mm4

#### Stress

Calculate the minimum and maximum stress at the base of the wall.

σMin =
N/mm2
σMax =
N/mm2 A compound section has been fabricated by means of attaching flange plates onto back to back parallel flange channels at the bottom and top. This section has been loaded with a total of three point loads. For the given case calculate the following:

• The second moment of area about the Z and Y Axes.
• The stress that is present at point A, B, C and D (The extents of the parallel flange channels).

### Solution

#### Second moment of area

Calculate the second moment of area about both axis, where Izz is the primary axis and Iyy is the secondary axis.

Izz =
mm4
Iyy =
mm4

#### Stress

Calculate the stress at the locations marked A, B, C and D.

σA =
N/mm2
σB =
N/mm2
σC =
N/mm2
σD =
N/mm2 A hollow steel vertical telegraph pole BC carries two groups of horizontal wires labelled E and D. The angles that these wires act at is shown in a plan view of the pole. These wires are acting in tension, in place to restrain the pole is a cable AC that is fixed at ground level. For the given case calculate the following:

• The second moment of area of the pole.
• The total axial stress, total bending stress and maximum tensile stress in the pole.

### Solution

#### Second moment of area

Calculate the second moment of area about the major axis - Izz.

Izz =
mm4

#### Stress

Calculate the total axial, bending and tensile stress.

Axial stress - σA =
mm4
Bending stress - σB =
mm4
Tensile stress - σT =
mm4 A gravity dam has been constructed to retain a mass of water using its self weight to resist the horizontal water pressure acting against it. For the given case calculate the following:

• The moments being applied onto the dam.
• The stress at location A and B.

Sketch the stress diagram indicating the values of the stress at location A and B.

### Solution

Calculate the Axial load due to self weight.

P =
kN

#### Moments

Calculate the Moments being applied to the dam.

MSW =
kNm
MVWater =
kNm
MHWater =
kNm

#### Stress

Calculate the stress at the locations marked A and B.

σA =
kN/m2
σB =
N/mm2