STUDENT NAMES:
Statics and Strength of Materials, Summer 2023
Topics: Chapters 15 (Deflections of Beams Due to Bending), and 17 (Design of Columns)
This is a team task.
Open book, open notes, no cell phone, no internet, no discussions with other student teams.
Typed solution expected. Draw sketches where necessary.
Correct choice of formulae, accurate calculations, appropriate units, well-drawn sketches, showing the work and clearly identifying your answers gets full grade for a question.
Answer all sub questions (if any) of a problem for full credit for that problem.
All questions are worth equal points
Identify your answers clearly.
1. Use the moment-area method to find:
(a) the maximum delection, and
(b) the slope at the free end of the cantilever beam shown in the figure below.
Draw the M/EI diagram by parts.
Assume that EI is constant
Neglect weight of the beam.
2. Use the moment-area method to find the delection at the middle of the simply supported beam shown in the figure below.
Draw the M/EI diagram by parts.
Assume that EI is constant.
Neglect weight of the beam.
3. A W360 x 110 rolled steel column has a length of 9.0m. The steel has a Young’s modulus of E = 200 x 106 kPa and a proportionality limit of P = 230 x 103 kPa. Use a factor of safety of 2. Determine the critical or Euler load and the allowable load if (a) the ends are pinned, (b) one end is pinned and the other end is fixed, and (c) both ends are fixed. For section properties, see Table A.3 (SI Units) of the Appendix (given below).
4. A boom consists of a 4 inch diameter steel pipe AB and a cable BC as shown in the figure below. The modulus of steel, E = 29 x 103 ksi. Dteremine the capacity P of the boom. Use the Euler formula with a factor of safety of 2.5. Neglect the weight of the pipe. Section properties of pipe are given as: A = 3.174 in.2, and the radius of gyration, r = 1.51 in.
