1.8 Practice Problems

Selected Problem Answers

  1. Briefly explain each of the following concepts.
    1. What does the constitutive model look like for a linear axial element in terms of stress and strain?
    2. What kind of support can resist a vertical load and moment, but not a horizontal load on a column? Draw such a support.
    3. What is the difference between the sign conventions for internal and external forces (in 2D)?
    4. Using the principle of slide-rule accuracy, round the following numbers to the correct level of precision and write them in engineering notation.
      1. $\SI{58920}{}$
      2. $\SI{1298.75}{}$
      3. $\SI{0.0008465}{}$
      4. $\SI{4698720}{}$
    5. What is the compatibility assumption with regard to the continuity of a beam?
  2. Draw the free body diagram for each of the systems shown below. Also draw the free body diagram of each system to the right of the indicated cut and show all unknown forces and moments in the element at the cut section.
  3. For each system from problem 2, find the reaction forces and the forces at the cut section if:
    1. $w=\SI{15}{kN/m}$, $L=\SI{8}{m}$, $x=\SI{3}{m}$
    2. $P_1=\SI{210}{kN}$, $P_2=\SI{300}{kN}$, $L=\SI{10}{m}$, $x=\SI{5}{m}$
    3. $w=\SI{24}{kN/m}$, $L=\SI{6}{m}$, $\theta=\ang{36.9}$, $x=\SI{4}{m}$
    4. $P=\SI{175}{kN}$, $L=\SI{6}{m}$, $h=\SI{3}{m}$, $\theta=\ang{30}$, $x=\SI{2}{m}$