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Moments

Content type
User Generated
Subject
Engineering
School
Catholic University of America
Type
Homework
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Q. 1.) A simply supported beam with a rectangular cross section shown below with h = 7.5 in, b = 2.75
in, is placed in bending with F=33 kip.
a. Calculate the reaction R
A
and R
B
b. Draw the shear force and bending moment diagram
c. Calculate the area Moment of Inertia I
z
[in
4
]
d. Calculate the Maximum bending stress s [psi] on the bottom surface using M
max
e. Calculate the Maximum transverse shear stress τ [psi] at the neutral axis [V
max
]
Solution:
a. 
  

 
 
 





 


 
















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b.





 










  





 










  

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Q. 1.) A simply supported beam with a rectangular cross section shown below with h = 7.5 in, b = 2.75 in, is placed in bending with F=33 kip. a. b. c. d. e. Calculate the reaction RA and RB Draw the shear force and bending moment diagram Calculate the area Moment of Inertia Iz [in4] Calculate the Maximum bending stress s [psi] on the bottom surface using Mmax Calculate the Maximum transverse shear stress τ [psi] at the neutral axis [Vmax] Solution: a. 𝐴𝑡 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚, 𝑤𝑒 𝑐𝑎𝑛 𝑎𝑝𝑝𝑙𝑦 𝑡ℎ𝑒 𝑓𝑜𝑟𝑐𝑒 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠: ∑ 𝐹𝑦 = 0 𝑖. 𝑒. 𝑠𝑢𝑚𝑚𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑓𝑜𝑟𝑐𝑒𝑠 𝑖𝑛 𝑦 − 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 = 0 𝑇ℎ𝑖𝑠 𝑚𝑒𝑎𝑛𝑠, 𝑅𝐴 + 𝑅𝐵 − 𝐹 = 0 𝑅𝐴 + 𝑅𝐵 = 𝐹 (1) 𝐴𝑙𝑠𝑜, ∑ 𝑀𝐴 = 0 𝑖. 𝑒. 𝑠𝑢𝑚𝑚𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑚𝑜𝑚𝑒𝑛𝑡𝑠 𝑎𝑏𝑜𝑢𝑡 𝑝𝑜𝑖𝑛𝑡 𝐴 = 0 𝑡ℎ𝑖𝑠 𝑚𝑒𝑎𝑛𝑠, 𝑅𝐵 (20 𝑓𝑡) − 𝐹𝑥 (7 𝑓𝑡) = 0 𝑅𝐵 (20) − 𝐹𝑥 (7) = 0 𝑹𝑩 = 𝟕𝑭 7(33) (↑) ≫ 𝑅𝐵 = = 𝟏𝟏. 𝟓𝟓 𝒌𝒊𝒑 (↑) 𝟐𝟎 20 𝑃𝑢𝑡𝑡𝑖𝑛𝑔 𝑖𝑛 (1) 𝑅𝐴 + 7𝐹 13𝐹 13(33) = 𝐹 ≫ 𝑅𝐴 = = = 𝟐𝟏. 𝟒𝟓 𝒌𝒊𝒑 (↑) 20 20 20 b. 𝑺𝒉𝒆𝒂𝒓 𝑭? ...
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