SOM Tutorial 1 (for discussion):
Topic 1: Internal reactions; stress for axial loads
Topic 2: Strain for axial loads: Hooke’s Law; shear stresses and strains; torsion
Question 1 (10.3)
Calculate the internal reactions for the member shown at the section MM & NN as shown in
Figure Q1.
Figure Q1
Solution:
Overall FBD:
From Static of Equilibrium:
∑𝐹𝑥 = 0; 𝐴𝑥 − 400 = 0
𝑨𝒙 = 𝟒𝟎𝟎 𝑵 →
∑𝐹𝑦 = 0; 𝐴𝑦 + 𝐵𝑦 − 200 = 0
𝐴𝑦 + 𝐵𝑦 = 200
∑𝑀𝐴 = 0; −200 × 8 + 𝐵𝑦 × 16 + 400 × 6 = 0
𝐵𝑦 = −50 𝑁
𝑩𝒚 = 𝟓𝟎 𝑵 ↓
𝐴𝑦 = 200 − 𝐵𝑦 = 200 − (−50)
𝑨𝒚 = 𝟐𝟓𝟎 𝑵 ↑
FBD Section MM
1
From Static of Equilibrium:
∑𝐹𝑥 = 0; 𝑉𝑀𝑀 − 400 = 0
𝑽𝑴𝑴 = 𝟒𝟎𝟎 𝑵 →
∑𝐹𝑦 = 0; 𝑭𝑴𝑴 = 𝟎
∑𝑀𝑀 = 0; 𝑀𝑀𝑀 + 400 × 3 = 0
𝑀𝑀𝑀 = −1200 𝑁 ∙ 𝑚
𝑴𝑴𝑴 = 𝟏𝟐𝟎𝟎 𝑵 ∙ 𝒎 𝑪𝑾
FBD Section NN
From Static of Equilibrium:
∑𝐹𝑥 = 0; 𝑭𝑵𝑵 = 𝟎
∑𝐹𝑦 = 0; 𝑉𝑁𝑁 − 50 = 0
𝑽𝑵𝑵 = 𝟓𝟎 𝑵
∑𝑀 𝑁 = 0; −𝑀𝑁 − 50 × 4 = 0
𝑀𝑁𝑁 = −200 𝑁 ∙ 𝑚
𝑴𝑵𝑵 = 𝟐𝟎𝟎 𝑵 ∙ 𝒎 𝑪𝑪𝑾
2
Question 2 (7-7)
Determine the resultant internal loadings in the beam at cross sections through points D and E.
Point E is just to the right of the 15-kN load.
Figure Q2
Solution:
CORRECTION: Bx = 0
3
Question 3 (7-26)
The built-up shaft consists of a pipe AB and solid rod BC. The pipe has an inner diameter of
20 mm and outer diameter of 28 mm. The rod has a diameter of 12 mm.
Determine the average normal stress at points D and E and represent the stress on a volume
element located at each of these points.
Figure Q5
Solution:
4
Question 4. Refer to figure Q4
a. Determine the maximum shearing stress caused by a 4.6-kN ⋅ m torque T in the 76mm-diameter shaft shown.
b. Solve part a, if the solid shaft has been replaced by a hollow shaft of the same outer
diameter (76-mm) and of 24-mm inner diameter.
Figure Q6
Solution:
5
Question 5 (7-74). Refer to figure Q5
The rectangular plate is subjected to the deformation shown by the dashed lines. Determine the
average shear strain 𝛾𝑥𝑦 in the plate.
Figure Q7.
Solution:
6
Question 6 (9-96). Refer to figure Q6
The 50-mm-diameter cylinder is made from Am 1004-T61 magnesium and is placed in the
clamp when the temperature is T1 = 20° C. If the 304-stainless-steel carriage bolts of the clamp
each have a diameter of 10 mm, and they hold the cylinder snug with negligible force against
the rigid jaws. Determine the force in the cylinder when the temperature rises to T2 = 130°C.
(𝐸magnesium = 44.7 GPa & 𝐸steel = 193 GPa)
Figure Q6.
Solution:
7