課程名稱︰鋼筋混凝土學
課程性質︰土木工程學系必修
課程教師︰歐昱辰
開課學院：工學院
開課系所︰土木工程學系
考試日期（年月日）︰2018/10/4~2018/10/11
考試時限（分鐘）：壹萬零捌十分鐘
試題 :
作業三(Homework three)
繳交日期(Due date):10/11
(1)若鋼筋混凝土梁矩形斷面為單筋梁，且配置單排鋼筋，斷面尺寸如下所示，混凝土規定
強度fc' = 280kgf/cm^2，鋼筋降伏強度fy = 4200kgf/cm^2。
https://imgur.com/J36yPNb （本人製圖）
(a)何謂平衡鋼筋比？
(b)此斷面之平衡鋼筋用量Asb為何？
(c)依此規範規定如何定義縱向鋼筋最大鋼筋比？
(d)此斷面之縱向鋼筋最大鋼筋量Asmax為何？
(e)規範限制最大鋼筋用量的目的為何？
(f)此斷面規範規定之最小鋼筋量Asmin為何？
(g)規範限制最小鋼筋用量的目的為何？
註：
(a)本題修改、合併自87年結構技師、99年與106年高考題。92年、98年、101年與104年普
考題。
(b)第(c)小題，目前規範沒有直接定義最大鋼筋比，而是定義εt有一最小值，此最小值
間接限制了最大可使用的鋼筋量。若為單排鋼筋，講義有推導最大鋼筋量的公式。
A singly reinforced concrete rectangular beam as shown above is designed
with one layer of longitudinal tension reinforcement. The concrete compress-
ive strength fc' = 280 kgf/cm^2. The reinforcement yield strength fy = 4200
kgf/cm^2.
(a)What is the balanced reinforcement ratio?(Definition)
(b)What is the balanced reinforcement area Asb of this beam?
(c)How is the maximum reinforcement ratio defined based on the code?
(d)What is the maximum reinforcement area Asmax for the longitudinal reinfo-
rcement of this beam?
(e)What is the perpose for the code to specify a maximum reinforcemant area?
(f)What is the minimum reinforcement area Asmin for the longitudinal reinfo-
rcement of this beam?
(g)What is the perpose for the code to specify a minimum reinforcement area?
Note:
(a)This question is modified from past nationa exams.
(b)For question (c), the code does not directly specify a maximum reinforce-
ment ratio. Instead, the code specifies a minimum value for εt, which indi-
rectly impose an upper limit on the longitudinal tension reinforcement. For
only one layer of longitudinal reinforcement, the lecture notes provide an
equation to calculate the maximum reinforcement ratio.
(2)下圖為兩端均為固定端之矩形斷面(35cm寬 x 70cm深)RC梁，梁淨跨度長L =7.5m，受
垂直均佈載重：靜載重wD = 8tf/m(含梁自重)與活載重wL = 7tf/m；梁跨中點彎矩採用
wL^2/24。拉力鋼筋之有效深度，統一取63cm作計算。混凝土fc' = 280kgf/cm^2，梁主
筋fy = 4200kgf/cm^2。
(見上面連結圖)
(a)計算跨度中央斷面所需拉力筋總面積。
(b)採#8鋼筋，每根斷面積Ab = 5.067cm^2，採單排配置，請決定至少需配置的根數。需
檢查淨間距是否符合規範規定，假設保護層厚度為4cm，採#3箍筋，最大粗粒料直徑為2cm。
(c)根據最終配置的拉力筋總面積As，檢查極限狀態εt是否滿足規範對梁的規定。
(d)檢查是否滿足規範最小鋼筋量規定。
(e)檢核φMn >= Mu。
註：
(a)本題修改、合併自90、91與105年結構技師、97、104與105年高考題。107年普考題。
(b)載重組合採1.2D+1.6L。
A RC beam as shown above is fixed at two ends and has a rectangular section
of 35 cm x 70 cm(width x height). The beam has a span L = 7.5m and is subje-
cted to vertical uniformly distributed loads: a dead load of wD = 8tf/m (in-
cluding the self-weight of the beam)and a live load of wL = 7tf/m. Use wL^2
/24 to calculate the moment at the mid span. The effective depth of the
beam is assumed to be 63 cm. Concrete fc' = 280 kgf/cm^2 and beam longitud-
inal reinforcement fy = 4200 kgf/cm^2.
(a)Calculate the required area of longitudinal tension reinforcement at the
midspan of the beam.
(b)Use #8 reinforcing bars for longitudinal reinforcement (Ab = 5.067 cm^2).
Use one layer design. Determine the minimum number of the reinforcing bars
to satisfy(a). Need to check the clear spacing of the bars based on the
code. Assume the cover depth is 4 cm. Use#3 transverse reinforcement. The
maximum size of the aggregate is 2 cm.
(c)Based on the final design of longitudinal reinforcement area As, check
whether εt at the ultimate state satisfies the code requirement on beams.
(d)Check the minimum reinforcement area based on the code.
(e)Check φMn >= Mu.
Note:
(a)This question is modified from past national exams.
(b)Use 1.2D+1.6L for the loading combination.