고체역학 assignment 1
1. A simply supported steel beam AB (Fig. 1a) of length L = 16 ft and height h = 12 in. is bent by couples 𝑀0
into a circular arc with a downward deflection δ at the midpoint(Fig. 1b). The longitudinal normal strain
(elongation) on the bottom surface of the beam is 0.00125, and the distance from the bottom surface of the beam
to the neutral surface is 6.0 in.
a) Determine whether it is pure bending or general loading and state the reason.
b) Determine the radius of curvature ρ, the curvature κ
c) Discuss the result of (b)
2. Determine the maximum tensile stress σ𝑡 (due to pure bending by positive bending moments M) for beams
having cross sections as follows (see figure 2): (a) a semi-circle diameter d, and (b) an isosceles trapezoid with
bases 𝑏1 = 𝑏 and 𝑏2 =
4𝑏
3
, and altitude h.
Figure 2
3. A simply supported wood beam AB with span length L = 4 m carries a uniform load of intensity q = 5.8 kN/m
(Figure 3). Calculate the maximum bending stress σmax due to the load q if the beam has a rectangular cross section
with width b = 140 mm and height h = 240 mm.
Figure 3
4. The simply supported beam shown in Figure 4. E = 2 x 1011 Pa.
a) What is the maximum tensile normal stress 𝜎𝑥𝑥 ?
b) What is the normal stress 𝜎𝑥𝑥 , 25 mm from the top of the section?
c) What is the radius of curvature of the neutral surface?
Figure 4
<과제 제출 시 주의 사항>
*글씨를 명확히 알아볼 수 있도록 작성
*이름, 학번을 표기할 것
*문제에 나온 기호 외에 임의로 기호 사용시 언급해 놓을 것
*제출 기한: 2021/9/23 (목) 23:59까지