臺灣博碩士論文加值系統

中文摘要
本論文研究主題為使用預力玻璃纖維(Prestressed Glass Fiber Reinforced Polymers－PGFRP)對鋼筋混凝土樑及空心圓形構件進行補強研究。近來，碳纖維複合材料已經被廣泛應用於受損害之鋼筋混凝土結構物之補強，但是因為碳纖維材料與混凝土材料之勁度相差太大，所以碳纖維複合材料對於 構件之預力轉移效果反而比較差，本篇論文選用玻璃纖維複合材料之原因是因為其彈性模數 與混凝土非常接近，對預力轉移效果極佳。本篇論文分二大主軸，第一主題為使用PGFRP對 樑之補強研究，第二主題為使用PGFRP對空心圓形構件之補強研究。
第一主題為採用玻纖及預力玻纖對 樑補強後之極限載重能力及變形性之試驗結果及理論比較。樑之型式採用T型及倒T型樑，當成是在壓力控制及拉力控制下之樑而進行試驗比較。試驗之預力玻纖布將被施加預拉力，其大小為其材料極限強度之一半。T型及倒T型樑在使用預力玻纖PGFRP之U型圍束補強後，其極限抗壓強度提高了2倍以上。而且使用PGFRP補強後之 樑將會拱起，但在拉力面不會產生裂縫。試驗結果顯示， T型樑在使用玻纖(GFRP)及預力玻纖(PGFRP)補強下，其極限抗彎矩強度分別提升至55%及100%；另倒T型樑在玻纖(GFRP)及預力玻纖(PGFRP)補強下，其極限抗彎矩強度分別提升至97%及117%；在相同的外加載重下，PGFRP 補強之樑比GFRP 補強之樑，其撓曲變形較小，顯示施加預力PGFRP補強之樑其變形會獲得較有效之控制。本研究之理論分析公式推導，先不受試驗結果之影響情況下獨立去探討前述各項補強之理論分析公式，並將理論分析公式與試驗結果比較，兩者之接近程度應可接受，在建議之安全係數下此理論公式可廣泛應用於GFRP及PGFRP對 樑之補強分析及設計。
第二主題為採用GFRP及PGFRP對空心及實心圓形構件之補強研究。本研究目的以實心及空心圓形構件模擬大型空心圓形管道結構，在遭受損壞後之補強研究。試驗結果顯示，包裹玻纖GFRP對 圓形實心或空心構件壓壞強度之提升效果非常顯著，即使是包裹事先已經被壓壞之試體，仍然可展現可觀之壓壞強度，例如GFRP包裹圓形實心試體，約略可提升200%強度，GFRP包裹圓形空心試體，更可提升至400%強度；PGFRP圍束補強相較於GFRP圍束補強， PGFRP對於構件之極限強度並無再提升作用，但對圓管側向勁度之提升卻有明顯效果，亦即PGFRP可控制圓形構件之側向變形性。理論分析所推導之各項公式，都與試驗結果頗為契合，在假設混凝土強度為210 情況下，試驗結果都比理論分析結果大，其差值約在10%之內。

ABSTRACT
The main topic of this dissertation is to use prestressed glass fiber reinforced polymers (PGFRP) to strengthen beams and hollow circular specimens. In these years, carbon fiber- reinforced polymer (CFRP) material has been popular used to repair or rehabilitate in deteriorated reinforced concrete ( ) structures. However, the stiffness variation between CFRP and concrete material lowers the effort in transferring the prestress from CFRP sheets to member. The reason for why this study chose glass fiber- reinforced polymers (GFRP) material was the Young’s modulus of GFRP material being quite close to concrete material. This dissertation was divided into two parts, Part I to study the strengthening of reinforced concrete ( ) beams using prestessed glass fiber-reinforced polymer (PGFRP) and Part Ⅱ to study the strengthening of hollow circular specimens using PGFRP.
The main subject of part Ⅰ of this dissertation is to compare the test and theoretical analysis strengthening results in using GFRP and PGFRP sheets for the load-carrying capacities (ultimate loads) and deflections of beams. Two beams shapes, T and -shaped, were used as the under-strengthened and over-strengthened beams. The GFRP sheets were prestressed to one-half their tensile capacities before bonded to the T and -shaped R. C. beams. The prestressed tensions in the PGFRP sheets caused cambers in R.C. beams without cracking on the tensile faces. The PGFRP sheets also enhanced the load-carrying capacities. The test results indicate that T-shaped beams with GFRP sheets exhibit an increase of load-carrying capacity by 55% while the same beams with PGFRP sheets can increase 100%. The -shaped beams with GFRP sheets can increase the load-carrying capacity by 97% while the same beams with PGFRP sheets increase the capacity by 117%. Under the same external loads, beams with GFRP sheets produce larger deflections than beams with PGFRP sheets. In the theoretical part, the equations obtained by theory match the test results quite well. It is suggested that this analytical method can be widely used for analyzing and designing beams strengthened using GFRP or PGFRP sheets.
The main subject of part Ⅱ of this dissertation is to study the strengthening of hollow and solid circular specimens using PGFRP. The purpose of this study is to strengthen the damaged solid and hollow circular specimens which were used to simulate the structures of large hollow circular pipes. The test results show that GFRP can increase a great deal of strength for specimens, even for the broken specimens. For instance, the solid specimens wrapped by GFRP can increase the strength around 200% and the hollow specimens wrapped by GFRP can even increase 400%. The results also show that PGFRP can’t increase more strength than GFRP. But PGFRP can increase the lateral stiffness of the specimens. In the

theoretical part, the equations obtained by theory match the test results very well. In this study, all the test results are greater than the theoretical results within a range of 10%.

總目錄
頁數
中文摘要　　　　　　　　　　　　　　　　　　　　　　　　　　　Ⅰ
ABSTRACT　　　　　　　　　　　　　　　　　　　　　　　　　　Ⅱ
總目錄　　　　　　　　　　　　　　　　　　　　　　　　　　　　Ⅳ
本文目錄　　　　　　　　　　　　　　　　　　　　　　　　　　　Ⅴ
表目錄　　　　　　　　　　　　　　　　　　　　　　　　　　　　Ⅷ
圖目錄　　　　　　　　　　　　　　　　　　　　　　　　　　　　Ⅸ
照片目錄　　　　　　　　　　　　　　　　　　　　　　　　　　　XI
符號說明　　　　　　　　　　　　　　　　　　　　　　　　　　 XIII















本文目錄
第一章 緒論 1
　　1-1 前 言 1
　　1-2 研究動機 1
　　1-3 研究目的 2
　　1-4 研究範圍 3
　　1-5 本文架構 3
第二章 文獻回顧 5
　　一、R.C.樑之補強研究 5
　　二、圓形構件之補強研究 7
第三章 R.C.樑應用玻纖補強之試驗及試驗結果 11
　　3-1 試驗計劃 11
　　　3-1-1 試驗構想 11
　　　3-1-2 試驗設備 11
　　　3-1-3 試驗材料 11
　　3-2 GFRP撓曲補強試驗步驟 12
　　　〈1〉T型樑試體規劃 12
　　　〈2〉倒T型樑試體規劃 13
　　　〈3〉GFRP施拉預力及轉移預力至R.C.樑過程 13
　　　〈4〉R.C.樑之彎曲試驗 14
　　3-3 試驗結果與討論 14
　　　〈1〉T型樑試驗結果 14
　　　〈2〉倒T型樑試驗結果 16
　　　〈3〉結論與討論 16


第四章 R.C.樑應用玻纖補強之理論分析並與試驗結果比較 30
　　4-1 撓曲補強之基本假設 30
　　4-2 T型樑與倒T型樑之理論撓曲強度(TRB,^RB) 30
　　4-3 GFRP應用於T型樑撓曲補強之理論分析(TFB) 32
　　4-4 PGFRP應用於T型樑撓曲補強之理論分析(TPFB) 36
　　4-5 GFRP應用於倒T型樑撓曲補強之理論分析(^FB) 37
　　4-6 PGFRP應用於倒T型樑撓曲補強之理論分析(^PFB) 38
　　4-7 理論分析並與試驗結果比較 38
　　〈1〉理論公式計算結果 38
　　〈2〉理論值與試驗值比較 45
第五章 圓形空心構件應用玻纖補強之試驗及試驗結果 51
　　5-1 試驗計畫 51
　　　5-1-1 試驗構想 51
　　　5-1-2 試驗設備 51
　　　5-1-3 試驗材料 52
　　　5-1-4 試體規劃 53
　　5-2 試驗項目與步驟 55
　　　5-2-1 圓形實心構件之壓壞試驗 55
　　　　〈1〉圓形純實心構件 55
　　　　〈2〉GFRP包裹實心構件 55
　　　　〈3〉GFRP包裹事先已破壞實心構件 55
　　　5-2-2 圓形空心構件之壓壞試驗 56
　　　　〈1〉圓形純空心構件 56
　　　　〈2〉GFRP包裹空心構件 56
　　　　〈3〉GFRP包裹事先已破壞空心構件 57
　　　　〈4〉PGFRP包裹空心構件 57
　　　　〈5〉PGFRP包裹事先已破壞空心構件 57
　　5-3 試驗結果與討論 57
　　　5-3-1 各項試驗之結果 57
　　　5-3-2 結論與討論 61
第六章 圓形空心構件應用玻纖補強之理論分析並與試驗結果比較 91
　　6-1 前言 91
　　6-2 圓形純空心構件之理論分析 91
　　6-3 GFRP包裹空心構件之理論分析 92
　　6-4 PGFRP包裹空心構件之理論分析 93
　　6-5 理論分析並與試驗結果比較 95
　　　〈1〉理論公式計算結果 95
　　　〈2〉理論值與試驗值比較 97
第七章 結論與建議 101
　　7-1 結論 101
　　7-2 建議 107
參考文獻 110










表目錄
表3-1 鋼筋、混凝土、碳纖維、玻璃纖維之材料的物理性質 18
表3-2 T型樑撓曲補強之試驗結果 18
表3-3 T型樑的變形及韌性比 19
表3-4 倒T型樑撓曲補強之試驗結果 19
表4-1 T型樑及倒T型樑破壞荷重和理論荷重之比較 47
表5-1 圓形實心構件之混凝土配比 63
表5-2 玻璃纖維材料(品牌一：TYFO)之物理性質 63
表5-3 TYFO玻璃纖維材料組成纖維之物理性質 64
表5-4 玻璃纖維材料(品牌二：L900-E)之物理性質 64
表5-5 環氧樹脂之性質 64
表5-6 圓形空心構件壓壞試驗試體之編號及尺寸 65
表5-7 圓形實心構件抗壓強度之試驗結果 65
表5-8 圓形空心構件壓壞試驗之試驗結果(H系列) 66
表5-9 圓形空心構件壓壞試驗之試驗結果(T系列) 66
表6-1 圓形空心構件破壞荷重試驗值及理論值比較 99










圖目錄
圖3-1 T型樑的斷面尺寸 20
圖3-2 T型樑的GFRP貼片型式及編號 20
圖3-3 倒T型樑的斷面尺寸 21
圖3-4 倒T型樑的GFRP貼片型式及編號 21
圖3-5 抗彎試體的載重方式 22
圖3-6 T型樑各組試體之荷重─變位圖 22
圖3-7 倒T型樑各組試體之試體的荷重─變位圖 23
圖4-1 T型樑未使用GFRP補強之中性軸在hf/b1上方之應力分佈圖 47
圖4-2 T型樑未使用GFRP補強之中性軸在hf/b1下方之應力分佈圖 48
圖4-3 混凝土之應力-應變關係圖(Kabaila et al.) 48
圖4-4 T型樑使用GFRP補強之中性軸在hf/b1上方之應力分佈圖 49
圖4-5 T型樑使用GFRP補強之中性軸在hf/b1下方之應力分佈圖 49
圖4-6 倒T型樑未使用GFRP補強之應力分佈圖 50
圖4-7 倒T型樑使用GFRP補強之應力分佈圖 50
圖5-1 純圓形實心構件 67
圖5-2 GFRP包裹圓形實心構件 67
圖5-3 混凝土空心構件之壓壞試驗 68
圖5-4 包裹GFRP之圓形空心構件壓壞試驗 68
圖5-5 圓形空心試體H1之壓壞試驗 69
圖5-6 圓形空心試體H2之壓壞試驗 69
圖5-7 圓心空心試體T1、T2、T3之壓壞試驗 70
圖5-8 圓形空心試體T1、T2、T3、T4之壓壞試驗(對數座標) 70
圖5-9 圓形空心試體HG1之壓壞試驗 71
圖5-10 圓形空心試體HG2之壓壞試驗 71
圖5-11 圓形空心試體FT1、FT2之壓壞試驗 72
圖5-12 圓形空心試體T與FT系列之壓壞試驗 72
圖5-13 圓形空心試體HG1-B之壓壞試驗 73
圖5-14 圓形空心試體HG2-B 之壓壞試驗 73
圖5-15 圓形空心試體(H系列)以GFRP材料補強之效果 74
圖5-16 圓形空心試體FTB1、FTB2之壓壞試驗 74
圖5-17 圓形空心試體FT1、FT2、FTB1、FTB2之比較 75
圖5-18 圓形空心試體PFT1-1.5、PFT2-1.5之壓壞試驗 75
圖5-19 圓形空心試體PFT1-3、PFT2-3之壓壞試驗 76
圖5-20 GFRP圓形空心試體有施加預力與無施加預力之比較 76
圖5-21 圓形空心試體PFTB1-1.5、PFTB2-1.5之壓壞試驗 77
圖5-22 圓形空心試體FTB與PFTB系列之壓壞試驗 77
圖5-23 圓形空心試體PFT與PFTB之壓壞試驗 78
圖6-1 複合材料圍束作用之自由體圖 99
圖6-2 圓管單位長度分析圖 100
圖6-3 半圓形分析圖 100
圖6-4 1/4圓形分析圖 100
圖6-5 理論推導之關係圖 100









照片目錄
照片3-1 50噸抗壓機 23
照片3-2 位移計和電子式測微計 24
照片3-3 7V14資料擷取系統 24
照片3-4 GFRP施加預力之油壓千斤頂 25
照片3-5 PGFRP試體的黏貼方式 25
照片3-6 TRB試體的破壞模式 26
照片3-7 TFB試體的破壞模式 26
照片3-8 TPFB試體的破壞模式 27
照片3-9 TPUFB試體的破壞模式 27
照片3-10 ^RB試體的破壞模式 28
照片3-11 ^FUB試體的破壞模式 28
照片3-12 ^PFB試體的破壞模式 29
照片5-1 試驗資料擷取之儀器 78
照片5-2 GFRP施加預力的千斤頂機器 79
照片5-3 純空心構件之壓壞試驗(H1) 79
照片5-4 純圓形空心構件(T系列) 80
照片5-5 單向編織之玻璃纖維布(L900-E) 80
照片5-6 包裹GFRP之空心圓管構件(FT系列) 81
照片5-7 GFRP包裹事先已破壞之圓形空心構件(FTB系列) 81
照片5-8 打磨混凝土試體表面 82
照片5-9 上膠前 82
照片5-10 上膠中 83
照片5-11 上膠後 83
照片5-12 PGFRP圓形空心試體施加預力玻纖之情況 84

照片5-13 PGFRP施加預力後、試體缺口圖 84
照片5-14 PGFRP施加預力後、試體缺口黏補後 85
照片5-15 純空心構件之壓壞試驗(T系列) 85
照片5-16 包裹GFRP空心圓管之壓壞試驗(HG1) 86
照片5-17 包裹GFRP空心圓管之壓壞試驗(FT系列) 86
照片5-18 GFRP包裹事先已破壞空心圓管之壓壞試驗(HG1-B) 87
照片5-19 GFRP包裹事先已破壞空心圓管之壓壞試驗(FTB系列) 88
照片5-20 PGFRP包裹圓形空心構件之壓壞試驗(PFT系列) 88
照片5-21 PGFRP包裹事先已破壞空心圓管之壓壞試驗(PFTB系列) 89
照片5-22 圓形空心試體抗壓試驗之破壞情況 89
照片5-23 圓形空心試體抗壓試驗之裂縫情況 90















符號說明
A’s = area of compression steel 壓力鋼筋之面積
As = area of tension steel 拉力鋼筋之面積
a = depth of Whitney rectangular stress block Whitney
矩形應力塊之深度
b = beam’s flange width 樑翼寬度
bw = beam web width 樑腹寬度
Cc = compression force resultant of concrete 混凝土壓力總合
Cs = compression force resultant of steel 鋼筋壓力總合
Cc1 = compression force resultant of concrete when the neutral
axis is located in the flange area and z is in the range of
0  z  x1= 當中性軸在樑翼內且0  z  x1時，混凝土壓力總合
Cc2 = compression force resultant of concrete when the neutral
axis is located in flange area and z is in range of x1  z  x
當中性軸在樑翼內且x1  z  x時，混凝土壓力總合
(Cc1)’ = compression force resultant of concrete in the part of bw
when the neutral axis is located in the web area and z is in the range of 0 z x1 當中性軸在腹版內且0  z  x1時，bw部份之混凝土壓力總合
(Cc2)’ = compression force resultant of concrete in the part of bw
when the neutral axis is located in web area and z is in range of x1  z  x 當中性軸在腹版內且x1  z  x時，bw部份之混凝土壓力總合
(Cc3)’ = compression force resultant of concrete in the part of (b-bw)
when neutral axis islocated in web area and z is in range of
0  z  x1 當中性軸在腹版內且0  z x1時，(b-bw)部份之混凝土壓力總合
(Cc4)’ = compression force resultant of concrete in the part of (b-bw)
when neutral axis islocated in web area and z is in range of
x1  z  x當中性軸在腹版內且x1  z  x時，(b-bw)部份之混凝土壓力總合
d = effective beam depth 樑有效深度
d’ = location of compression steel 壓力筋之深度
Ec = concrete Young’s modulus 混凝土彈性模數
Epl = young’s modulus of FRP plate FRP貼片之彈性模數
Es = steel Young’s modulus 鋼筋之彈性模數
e = eccentric distance of the preload from section’s centroid
從斷面形心至預力處之偏心矩
fc = compression stress of concrete 混凝土之壓應力
fc’ = compression strength of concrete 混凝土之抗壓強度
f’s = steel stress, 鋼筋之應力
fy = yield strength of steel 鋼筋之降服強度
h = entire height of R.C. beam R.C.樑之總深度
hf = flange thickness 翼版之厚度
Mn = nominal moment of the beam 樑之標稱彎矩強度
P = preload to the beam 施拉之預力
tpl = thickness of FRP plate FRP貼片之厚度
x = location of the neutral axis 中性軸之位置
x1 = location where the concrete strain is 0.002
混凝土應變量為0.002之位置
= acting location of force Cc1 ， Cc1之作用力位置
= acting location of force Cc2 ， Cc2之作用力位置
= acting location of force Cc3， Cc3之作用力位置
= acting location of force Cc4 ， Cc4之作用力位置
z = any arbitrary location of concrete 混凝土之任意位置
1 = 0.85-0.05 , f’c in MPa. 混凝土係數
c = concrete strain, 混凝土之應變
pl = strain of FRP plate FRP貼片之應變
(pl)u = ultimate strain of FRP plate FRP之極限應變
uc = concrete ultimate strain, 0.003 混凝土極限應變0.003
’s = strain of compression steel 鋼筋之極限應變
y = yield strain of steel, 鋼筋之降服應變

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