Reaction Calculations for Simply supported beams    

Part A – Reaction Calculations for Simply supported beams                (Total 25)

Problem 1[1]                                                                                                     (20 Marks)

1. For the beams a and b shown in Figure 1a and Figure 1b respectively:
2. Clearly present the Free Body Diagram (FBD) of the beam (8Marks)
3. Calculate the Reactions at the Supports A and B and carry out checks (12Marks)

For loading use the following:

Point load (P):                       1^st and 2^nd digit of your student number (for example if SN: 123456, PL=12kN)

For UDL:                                The last digit of your student Number

Simply Supported Beam a

Figure 1a – Simply supported beam loaded with inclined point load (P) and Uniformly Distributed Load (UDL)

 Simply Supported with Cantilever Beam b

Figure 1b – Simply supported beam loaded with inclined point load (P) and Uniformly Distributed Load (UDL)

Problem 2[2]                                                                                                     (5 Marks)

2a. For the Cantilever beam shown in Figure 2:

1. Clearly present the Free Body Diagram (FBD) of the beam
2. Calculate the Reactions at the fixed Supports A

For loading use the following:

Point load (P):           1^st and 2^nd digit of your student number (for example if SN: 123456, PL=12kN)

Cantilever Beam C

Figure 2 – Cantilever beam loaded point load (P)

Important information!

Brief Answer table[3]:

Part B – Reaction Calculations for Frames                                               (Total 15 Marks)

Problem 3[4]

3. For the rigid frame shown in Figure 3:
4. Clearly present the Free Body Diagram (FBD) of the beam
5. Calculate the Reactions at the Supports A and B and carry out checks

Figure 3 – Rigid frame loaded with Uniformly Distributed Load and point load (P)

For loading use the following:

Point load (P):                       1^st and 2^nd digit of your student number (for example if SN: 123456, PL=12kN)

For UDL:                                The 4^th digit of your student Number

Brief Answer table:

Part C – Design Diagrams of simply supported beams                           (40 Marks)

Problem 1[5]

1. For the beams a and b shown in Figure 1a and Figure 1b respectively:
2. Clearly present the Free Body Diagram (FBD) of the beam
3. Calculate the Reactions at the Supports A and B and carry out checks
4. Calculate and Design the Bending Moment Diagram (BMD)
5. Calculate and Design the Shear Forces Diagram (SFD)

For loading use the following:

Point load (P):           1^st and 2^nd digit of your student number (for example if SN: 123456, PL=12kN)

For UDL:                    The last digit of your student Number

Simply Supported Beam a

                                                                           (15 Marks)

Figure 1a – Simply supported beam loaded with inclined point load (P) and Uniformly Distributed Load (UDL)

 Simply Supported with Cantilever Beam b                                              (20 Marks)

Figure 1b – Simply supported beam loaded with inclined point load (P) and Uniformly Distributed Load (UDL)

Brief Answer table:

Problem 2[6]                                                                                                     (5 Marks)

2a. For the Cantilever beam shown in Figure 2:

1. Clearly present the Free Body Diagram (FBD) of the beam
2. Calculate the Reactions at the fixed Supports A
3. Calculate and Design the Bending Moment Diagram (BMD)
4. Calculate and Design the Shear Forces Diagram (SFD)

2b. Determine the bending deflection at mid span in the same beams: Assuming constant E Modulus of Elasticity and I moment of Inertia

For loading use the following:

Point load (P):                       1^st and 5^th digit of your student number

Cantilever Beam C

Figure 2 – Cantilever beam loaded point load (P)

Brief Answer table:

Part d – Reaction and Design Diagrams of three pin – frame                  (20 Marks)

4. For the three pin frame shown in Figure 4:
5. Clearly present the Free Body Diagram (FBD) of the beam
6. Calculate the Reactions at the Supports A and B and carry out checks
7. Calculate and Design the Bending Moment Diagram (BMD)
8. Calculate and Design the Shear Forces Diagram (SFD)
9. Critically evaluate the results and commend on the results

Point load (P):           1^st and 2^nd digit of your student number (for example if SN: 123456, PL=12kN)

For UDL:                    The last digit of your student Number

Figure 4 – Three pin frame loaded with Uniformly Distributed Load and point load (P)

Brief Answer table:

[1] P1a and P1b for Simply Supported beams

[2] P1a and P2a for Cantilever beams

[3] Provide all answers in the brief table. Amend table by adding or deleting, if necessary, rows or columns to enter all calculated answers. Calculations processes will not be checked for any answer given for values that are not booked in the brief table.

[4] P1a and P1b for Rigid Frames

[5] P1a and P1b for Simply Supported beams

[6] P1a and P2a for Cantilever beams