# Shear and Bending Tutorial Questions

These tutorial questions consider statically determinate simply supported beams subjected to a variety of loading conditions. They get progressivly more complex and are designed to be worked through sequentially. When selected, the span and loading conditions 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) - 1 decimal place.
• Bending moments (kNm) - 1 decimal place.
• Dimensions (m) - 3 decimal places.
• Numeric answers are required in all the fields. If you calculate a force or a moment 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.

• UDL - Universally Distributed Load; magnitude of load remains uniform throughout the length of the beam.
• PL - Point Load; concentrated load acting over a small distance, can be considered to be acting on a point.
• PUDL - Partial Universally Distributed Load; magnitude of load remains uniform throughout a portion length of the beam.
• TDL - Triangular Distributed Load; magnitude of load remains uniform throughout a portion length of the beam.
• TRDL - TRapezoidal Distributed Load; magnitude of load remains uniform throughout a portion length of the beam.

#### Q1 : UDL only.

For the simply supported beam, calculate the following:

• The horizontal reactions.
• The vertical reactions.
• The position and magnitude of the maximum bending moment.

Sketch the shear force and bending moment diagrams and the deflected shape of the beam. Your sketches should indicate the values of the shear force at the critical locations and the magnitude/position of the maximum bending moment.

@ A - Ha = kN
@ B - Hb = kN

@ A - Va = kN
@ B - Vb = kN

X (from A) m
MEd @ X = kNm

#### Q2 : Single PL.

For the simply supported beam, calculate the following:

• The horizontal reactions.
• The vertical reactions.
• The position and magnitude of the bending moment at the position where the point load acts i.e at the point marked 1.
• The position and magnitude of the bending moment at the position where the point load acts i.e at the point marked 1.

Sketch the shear force and bending moment diagrams and the deflected shape of the beam. Your sketches should indicate the values of the shear force at the critical locations and the magnitude/position of the maximum bending moment.

@ A - Ha = kN
@ B - Hb = kN

@ A - Va = kN
@ B - Vb = kN

#### Shear Force

Maximum and minimum shear force at the point marked 1.

@ 1Max = kN
@ 1Min = kN

#### Bending Moment

Maximum bending moment at the point marked 1.

MEd @ 1 = kNm

#### Q3 : Cantilever to right, UDL & single PL.

For the simply supported beam, calculate the following:

• The horizontal reactions.
• The vertical reactions.
• The position and magnitude of the maximum bending moment.

Sketch the shear force and bending moment diagrams and the deflected shape of the beam. Your sketches should indicate the values of the shear force at the critical locations and the magnitude/position of the maximum bending moment.

@ A - Ha = kN
@ B - Hb = kN

@ A - Va = kN
@ B - Vb = kN

#### Shear Force

Maximum and minimum shear force at the support B.

@ BMax = kN
@ BMin = kN

#### Bending Moment

The position and magnitude of the maximum bending moment in the main span between supports A & B.

X (from A) m
MEd @ X = kNm

The magnitude of the maximum bending moment at the support B.

MEd @ B m

#### Point of Contraflexure between A & B

Calculate the position of the point of contraflexure between the supports A & B.

XPOC (from A) m

#### Q4 : Cantilever to right, PUDL & 2 No. PL's.

For the simply supported beam, calculate the following:

• The horizontal reactions.
• The vertical reactions.
• The position and magnitude of the maximum bending moment.

Sketch the shear force and bending moment diagrams and the deflected shape of the beam. Your sketches should indicate the values of the shear force at the critical locations and the magnitude/position of the maximum bending moment.

@ A - Ha = kN
@ B - Hb = kN

@ A - Va = kN
@ B - Vb = kN

X (from A) m
MEd @ X = kNm

#### Q5 : Cantilever to both ends, PUDL & 2 No. PL's.

For the simply supported beam, calculate the following:

• The horizontal reactions.
• The vertical reactions.
• The position and magnitude of the maximum bending moment.

Sketch the shear force and bending moment diagrams and the deflected shape of the beam. Your sketches should indicate the values of the shear force at the critical locations and the magnitude/position of the maximum bending moment.

@ A - Ha = kN
@ B - Hb = kN

@ A - Va = kN
@ B - Vb = kN

X (from A) m
MEd @ X = kNm

#### Q6 : Single TRDL.

For the simply supported beam, calculate the following:

• The horizontal reactions.
• The vertical reactions.
• The position and magnitude of the maximum bending moment.

Sketch the shear force and bending moment diagrams and the deflected shape of the beam. Your sketches should indicate the values of the shear force at the critical locations and the magnitude/position of the maximum bending moment.

@ A - Ha = kN
@ B - Hb = kN

@ A - Va = kN
@ B - Vb = kN

X (from A) m
MEd @ X = kNm

#### Q7 : Cantilever to right, TRDL & single inclined PL.

For the simply supported beam, calculate the following:

• The horizontal reactions.
• The vertical reactions.
• The position and magnitude of the maximum bending moment.

Sketch the shear force and bending moment diagrams and the deflected shape of the beam. Your sketches should indicate the values of the shear force at the critical locations and the magnitude/position of the maximum bending moment.

@ A - Ha = kN
@ B - Hb = kN

@ A - Va = kN
@ B - Vb = kN

X (from A) m
MEd @ X = kNm

#### Q8 : Cantilever to both ends, 2 No. PUDL's & 2 No. PL's.

For the simply supported beam, calculate the following:

• The horizontal reactions.
• The vertical reactions.
• The position and magnitude of the maximum bending moment.

Sketch the shear force and bending moment diagrams and the deflected shape of the beam. Your sketches should indicate the values of the shear force at the critical locations and the magnitude/position of the maximum bending moment.

@ A - Ha = kN
@ B - Hb = kN

@ A - Va = kN
@ B - Vb = kN

X (from A) m
MEd @ X = kNm

#### Q9 : Cantilever to right, PUDL & TDL & single inclined PL.

For the simply supported beam, calculate the following:

• The horizontal reactions.
• The vertical reactions.
• The position and magnitude of the maximum bending moment.

Sketch the shear force and bending moment diagrams and the deflected shape of the beam. Your sketches should indicate the values of the shear force at the critical locations and the magnitude/position of the maximum bending moment.

@ A - Ha = kN
@ B - Hb = kN

@ A - Va = kN
@ B - Vb = kN

X (from A) m
MEd @ X = kNm

#### Q10 : Cantilever with PUDL & inclined PL.

For the simply supported beam, calculate the following:

• The horizontal reactions.
• The vertical reactions.
• The position and magnitude of the maximum bending moment.

Sketch the shear force and bending moment diagrams and the deflected shape of the beam. Your sketches should indicate the values of the shear force at the critical locations and the magnitude/position of the maximum bending moment.

@ A - Ha = kN
@ B - Hb = kN

@ A - Va = kN
@ B - Vb = kN

X (from A) m
MEd @ X = kNm