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井下水準(zhǔn)測量實(shí)習(xí)報(bào)告

網(wǎng)站:公文素材庫 | 時(shí)間:2019-05-28 14:15:13 | 移動(dòng)端:井下水準(zhǔn)測量實(shí)習(xí)報(bào)告

井下水準(zhǔn)測量實(shí)習(xí)報(bào)告

第五章井下水準(zhǔn)測量

一、實(shí)驗(yàn)?zāi)康?/p>

井下高程測量的目的是在井下建立一個(gè)與地面統(tǒng)一的高程系統(tǒng),確定各種采掘巷道峒,在豎直方向上的位置及相互關(guān)系。其任務(wù)是:1、確定主要巷道內(nèi)各水準(zhǔn)點(diǎn)與導(dǎo)線點(diǎn)的高程,已建立井下高程基本控制;2、給定巷道在豎直面內(nèi)的方向;3、測繪主要運(yùn)輸巷道縱剖面圖;井下高程測量分三種類型;1、通過立井導(dǎo)入高程;2、水準(zhǔn)測量;3、三角高程測量。試驗(yàn)在黑暗環(huán)境中進(jìn)行,要求學(xué)生掌握在該環(huán)境下作業(yè)的方法與技巧。

二、實(shí)驗(yàn)原理

在進(jìn)行井下高程測量之前,在井底車場和主要巷道內(nèi)預(yù)先設(shè)置好水準(zhǔn)點(diǎn),水準(zhǔn)點(diǎn)每組應(yīng)不少兩個(gè),兩點(diǎn)距離在30到80米;各組之間的距離一般是300到800米范圍之內(nèi)。井下永久導(dǎo)線點(diǎn)可做水準(zhǔn)點(diǎn)用,水準(zhǔn)點(diǎn)應(yīng)編號。

井下水準(zhǔn)測量分為兩級:I級水準(zhǔn)測量時(shí)井下高程測量的首級控制,其精度較高,基本上滿足貫通工程在高程方面上的精度要求,一般由井底車場水準(zhǔn)點(diǎn)開始,沿主要運(yùn)輸巷道想井田邊界敷設(shè);II級水準(zhǔn)測量的精度較低,作為I級水準(zhǔn)點(diǎn)間的加密控制,主要滿足礦井日常生產(chǎn)需要。一般在主要巷道掘進(jìn)是,先用II級水準(zhǔn)給腰線。當(dāng)巷道掘進(jìn)到300~800米時(shí),在測設(shè)I級水準(zhǔn)點(diǎn),以確定在巷道中設(shè)置水準(zhǔn)點(diǎn)和永久導(dǎo)線點(diǎn)的高程,并作為對II級水準(zhǔn)點(diǎn)的檢查。這樣逐漸向前測設(shè),直到井田邊界為止。當(dāng)井田一翼小于800米可不測I級水準(zhǔn)。井下水準(zhǔn)測量的施測方法為:視線長度宜為15~40米;前后視距大致相等;每站用兩次儀器高法觀測,其高差互差I(lǐng)級為4毫米,II級為5毫米取其平均值為一次測量結(jié)果。當(dāng)水準(zhǔn)點(diǎn)設(shè)在巷道頂板上時(shí),要倒立水準(zhǔn)尺,讀數(shù)應(yīng)加“”號。

I級水準(zhǔn)路線應(yīng)用兩次儀高法沿線路往返測量;II級閉、附和水準(zhǔn)路線可用兩次儀高法進(jìn)行單程測量。水準(zhǔn)測量的高程容許閉合差,見下:

水準(zhǔn)測量等級水準(zhǔn)支線往返的高差不符值閉、附路線的高程容許閉合差

I+15mm/-15mm倍的根號下R

II+30mm/-30mm倍的根號下R正負(fù)24mm倍的根號下L三、實(shí)驗(yàn)內(nèi)容與要求

1、從教學(xué)區(qū)一號樓與二號樓之間的水準(zhǔn)點(diǎn)出發(fā),通過學(xué)校的人防巷道,再返回,形成一個(gè)閉合的水準(zhǔn)路線。

2、本實(shí)驗(yàn)按照II級水準(zhǔn)測量的要求和精度作業(yè)。

四、注意事項(xiàng)

1、保證儀器安全;

2、全組同學(xué)精密組織;

3、實(shí)驗(yàn)前認(rèn)真復(fù)習(xí)有關(guān)內(nèi)容。

五、實(shí)驗(yàn)數(shù)據(jù)及處理測點(diǎn)上絲讀數(shù)下絲讀數(shù)后視距離前視距離視距差后視讀數(shù)前視讀數(shù)高差兩次高差之差高差中數(shù)±5mm累積高差站號1A-1.108-1.21120.6-0.6-1.108-0.966-0.1423-0.144-0.144BA-0.860-1.072-0.956-1.16521.220.90-1.061-0.916-0.145B2B-0.812-1.021-0.887-1.18220.929.5+1.528.029.3+1.128.225.6-0.8-1.132-1.364+0.23226.425.9-0.2-1.235-1.468+0.23426.1-2+0.233-0.033-0.954-0.834-0.120-1.035-0.912-0.123-3-0.122-0.266CB-0.872-1.052-0.808-1.101C3C-0.793-0.975-1.006-1.270DC-1.232-1.496-1.111-1.350D-1.338-1.5994DE-0.867-1.023-0.996-1.15915.616.3-0.7-0.945-1.077+0.132+2+0.131+0.163DE-1.046-1.204-1.175-1.33615.816.1-0.3-1.125-1.255+0.1305EF-0.678-0.857-0.518-0.69818.918.0+0.9-0.762-0.608-0.154+1-0.154+0.011EF-0.851-1.039-0.70018.818.1+0.7-0.945-0.790-0.1-0.8816FG-0.876-1.112-1.054-1.274FG-0.558-0.992-0.782-1.00422.223.4+1.4-0.725-0.893+0.16822.023.6+1.6-0.994-1.164+0.170+20.169+0.180

測量線路略圖

擴(kuò)展閱讀:4等水準(zhǔn)測量實(shí)習(xí)報(bào)告(僅供學(xué)習(xí)交流)

實(shí)習(xí)報(bào)告

(201*年6月02日6月15日)

課程名稱:鐵路工程測量放線系(部):交通系班級:11022班","p":{"h":23.662,"w":5.915,

目錄

第一部分四等水準(zhǔn)測量...............................................................................................1

1.1、實(shí)習(xí)目的...........................................................................................................21.2、儀器設(shè)備...........................................................................................................2

1.3、實(shí)習(xí)任務(wù)...........................................................................................................21.4、實(shí)習(xí)要點(diǎn)及流程................................................................................................21.5、注意事項(xiàng)...........................................................................................................31.6、數(shù)據(jù)記錄及處理................................................................................................41.7、誤差及誤差分析................................................................................................62.1、實(shí)習(xí)目的...........................................................................................................82.2、儀器設(shè)備...........................................................................................................82.3、實(shí)訓(xùn)任務(wù)...........................................................................................................82.4、數(shù)據(jù)計(jì)算..........................................................................................................102.5、測量方法..........................................................................................................182.6、誤差以及誤差分析............................................................................................18第三部分橋梁施工測量................................................................................................19

3.1、實(shí)習(xí)目的..........................................................................................................193.2、儀器設(shè)備..........................................................................................................19

3.3、實(shí)訓(xùn)任務(wù)..........................................................................................................193.4、曲線數(shù)據(jù)計(jì)算...................................................................................................213.6、測量方法..........................................................................................................33參考文獻(xiàn).........................................................................................................................34

摘要

本次實(shí)習(xí)共有三個(gè)內(nèi)容,一是四等水準(zhǔn)測量,這個(gè)要求我

們數(shù)量的掌握水準(zhǔn)儀的使用方法,以及如何讀書,還有就是注意兩個(gè)不同尺子的位置,如果漏掉其中的一項(xiàng),就會(huì)出現(xiàn)錯(cuò)誤,易導(dǎo)致數(shù)據(jù)不對,還得重測。測量時(shí)記錄數(shù)據(jù)的人是關(guān)鍵,他必須立刻計(jì)算出來,看黑面尺的讀書經(jīng)過紅面尺的檢查是否正確,還要控制前后視距差不要超限,隨時(shí)告訴測量者調(diào)整前后視距差,當(dāng)然,若想取得好的成果,還要每個(gè)人的配合,只有團(tuán)隊(duì)的合作,才能取得成功。

二是線路施工測量,這個(gè)任務(wù)和水準(zhǔn)的截然相反,水準(zhǔn)測量是先測完后在計(jì)算內(nèi)業(yè),而這個(gè)是先進(jìn)行大量的數(shù)據(jù)處理,求出每個(gè)點(diǎn)的曲線坐標(biāo)和邊莊坐標(biāo),才能進(jìn)行野外的實(shí)習(xí),如果內(nèi)業(yè)沒計(jì)算好,那么外業(yè)的工作就一點(diǎn)也沒法做,外業(yè)時(shí)應(yīng)注意,首先把儀器擺放好,這要求我們應(yīng)熟練地掌握全站儀的使用方法,立棱鏡的人應(yīng)把棱鏡立直,不然誤差很大。

三是橋梁墩臺(tái)的測設(shè),這個(gè)和線路施工測量差不多,就是內(nèi)業(yè)處理上不同,外業(yè)上都一樣,至于內(nèi)業(yè)上如何處理,后面將做詳細(xì)的介紹。

關(guān)鍵詞:水準(zhǔn)測量、線路施工測量、橋梁墩臺(tái)測設(shè)、團(tuán)隊(duì)協(xié)作。

第一部分四等水準(zhǔn)測量

1.1、實(shí)習(xí)目的

(1)熟悉水準(zhǔn)儀的使用。

(2)掌握四等水準(zhǔn)測量的觀測、記錄、計(jì)算的方法。

(3)熟悉四等水準(zhǔn)測量的主要技術(shù)指標(biāo),掌握測站及水準(zhǔn)路線的檢核方法。

1.2、儀器設(shè)備

每組DS3水準(zhǔn)儀1臺(tái)、雙面尺2把、記錄板1個(gè)。

1.3、實(shí)習(xí)任務(wù)

1、按四等水準(zhǔn)測量方法,施測一條閉合水準(zhǔn)路線,路線長度652.3m,16個(gè)測站。2、高差閉合差限差四等為Fh=±20L(mm)。3、編寫實(shí)訓(xùn)總結(jié)

1.4、實(shí)習(xí)要點(diǎn)及流程

(一)擬定施測路線

自行選一已知水準(zhǔn)點(diǎn)作為高程起始點(diǎn)BM1,選擇一定長度一定高差的路線作為施測水準(zhǔn)路線,形成一條閉合水準(zhǔn)路線。

要求不少于15個(gè)測站,1人觀測、1人記錄、2人立尺,施測完畢后應(yīng)輪換工種。(二)觀測方法

1、四等水準(zhǔn)測量測站觀測程序如下(后、后、前、前或黑、紅、黑、紅):(1)瞄準(zhǔn)后視標(biāo)尺黑面,精平,讀取下絲、上絲、中絲讀數(shù),記為1、2、3;(2)瞄準(zhǔn)后視標(biāo)尺紅面,精平,讀取中絲讀數(shù),記為4;

(3)瞄準(zhǔn)前視標(biāo)尺黑面,精平,讀取下絲、上絲、中絲讀數(shù),記為5、6、7;(4)瞄準(zhǔn)前視標(biāo)尺紅面,精平,讀取中絲讀數(shù),記為8。

2、三等水準(zhǔn)測量測站觀測程序?yàn)楹、前、前、后或黑、黑、紅、紅。(三)一個(gè)測站上的計(jì)算檢核1、視距計(jì)算檢核

后視距離9=(1-2)×100

前視距離10=(6-5)×100(三等<75m,四等<100m)前后視距差11=9-10(三等<3m,四等<5m)前后視距累差12=本站11+上站12(三等<6m,四等<10m)2、同一水準(zhǔn)尺紅、黑面讀數(shù)差檢核后尺紅黑面讀數(shù)差13=3+K-4

前尺紅黑面讀數(shù)差14=7+K-8(三等<2mm,四等<3mm)3、高差的計(jì)算和檢核黑面高差15=3-7紅面高差16=4-8

黑紅面高差之差17=15-16±0.1=13-14(三等<3mm,四等<5mm)4、計(jì)算平均高差

平均高差18=(15+16±0.1)÷2(四)總的計(jì)算和檢核1、視距的計(jì)算和檢核末站12=Σ9Σ10總視距=Σ9+Σ102、高差的計(jì)算和檢核

測站為偶數(shù)時(shí):總高差=Σ18=(Σ15+Σ16)÷2〔Σ(3+4)Σ(7+8)〕÷2測站為奇數(shù)時(shí):總高差=Σ18=(Σ15+Σ16±0.1)÷2

1.5、注意事項(xiàng)

1、一般注意事項(xiàng)與五等水準(zhǔn)測量一樣。

2、施測中每一站均需現(xiàn)場進(jìn)行測站計(jì)算和校核,確認(rèn)測站各項(xiàng)指標(biāo)均合格后才能遷站。水準(zhǔn)測量完成后,應(yīng)計(jì)算水準(zhǔn)路線高差閉合差,高差閉合差小于允許值方可收測,否則,應(yīng)查明原因,返工重測。

3、實(shí)訓(xùn)中勿專門化作業(yè),小組成員的工種應(yīng)進(jìn)行輪換,保證每人都能擔(dān)任到每一項(xiàng)工種。

4、測站數(shù)一般應(yīng)設(shè)置為偶數(shù);為確保前、后視距離大致相等,可采用步測法;同時(shí)在施測過程中,應(yīng)注意調(diào)整前后視距,以保證前后視距累計(jì)差不超限。

1.6、數(shù)據(jù)記錄及處理

四等水準(zhǔn)測量記錄簿

日期:201*年6月9日天氣:晴儀器型號:DS3組號:7

觀測:范永斌記錄:范增香司尺:鄭一超劉志復(fù)核:張煥軍后下絲前下絲水準(zhǔn)尺讀數(shù)方向K+黑高差測點(diǎn)尺上絲尺上絲及減紅中數(shù)黑面紅面編號后視距備注前視距尺號(mm)(m)(m)(m)視距差d∑d測站編號129111.4061.29717.7-0.61.3215610121.3871.26918.3-0.61.3591.20315.6-2.21.4681.31515.3-31.4401.29614.4-2.21.3761.21616-51.3561.20315.3-5.41.3311.17615.5-61.432后前后-前后7前8后-前后8前7后-前后7前8后-前后8前7后-前后7前8后-前后8前7后-前后7前8后-前后81BM1|Z12Z1|Z21.17814.3-1.31.4621.31714.5-0.81.4621.31115.1-1.11.3343Z2|Z34Z3|Z45Z4|Z51.201*3.3-2.71.3971.24814.9-0.41.4311.28214.9-0.61.3076Z5|Z67Z6|Z7Z7837151.3521.3280.0241.2561.284-0.0281.3901.392-0.0021.3871.3690.0181.2701.296-0.0261.3211.2790.0421.3571.2530.1041.2364

48166.0396.114-0.0756.0405.9700.076.0776.178-0.1016.1746.0550.1995.9566.082-0.1265.9685.9680.1416.0446.0400.0046.02213141701-13-1201-101-1110-1-210001180.0245K7=4.687K8=4.787-0.029-0.00150.0185-0.0260.04150.104-0.11

|Z81.16813.9-1.61.4111.27715.5-7.61.3081.14816-9.51.3641.22613.8-5.51.3791.21816.1-7.21.3281.14218.6-5.21.4651.27216-21.4421.29015.2-0.21.5341.374161.31.5391.36617.30.81.5091.32713.24.2前7后-前后7前8后-前后8前7后-前后7前8后-前后8前7后-前后7前8后-前后8前7后-前后7前8后-前后8前7后-前后7前8后-前9Z8|Z91.27014.1-1.91.5171.33917.841.41910Z9|Z1011Z10|Z111.27514.4-1.71.3871.18120.621.4381.24619.23.21.44012Z11|Z1213Z12|Z1314Z13|Z141.270171.81.4211.24617.51.51.4801.31216.8-0.51.4401.27416.63.415Z14|Z15Z15|Z16Z16|BM1161.3536.040-0.117-0.0181.3396.0271.2286.0140.1110.0131.4306.2161.2955.9820.0540.2341.3496.0351.2996.0840.05-0.0491.3286.0701.2355.9210.0490.1491.3426.0291.3056.171-0.0431-0.1421.3546.1311.3686.056-0.0140.0751.3336.0211.4546.241-0.121-0.221.3976.1831.4536.140-0.0460.0431.3576.0441.443-0.0866.228-0.18401-11-210112-111001-12-13-10-11-1202-20.1120.094-0.01150.049-0.0425-0.0195-0.12050.051517-0.085

檢核1∑9=265.8(∑15+∑16)=+0.001∑10=261.62∑9-∑10=4.2末站12=4.2總視距=∑9+∑10=527.4∑18=+0.001fhh2.5mmFh40L33.70mmfhFh測量精度合格

1.7、誤差及誤差分析

在測量工作中由于儀器、人、環(huán)境等各種因素的影響,使測量成果中都帶有誤差。為了保證測量成果的精度,需要分析研究產(chǎn)生誤差的原因,并采取措施消除和減小誤差的影響。水準(zhǔn)測量中誤差的主要來源有:

一、儀器誤差:

誤差視準(zhǔn)軸與水準(zhǔn)管軸不平行引起的誤差(i角誤差)調(diào)焦引起誤差水準(zhǔn)尺的誤差二、觀測誤差:

誤差氣泡居中的誤差估讀水準(zhǔn)尺分劃的誤差扶水準(zhǔn)尺不直的誤差

改正方法對視線長加以限制消除視差水準(zhǔn)尺最好裝有水準(zhǔn)器;搖尺法前后視距相等前后視距相等使用前檢驗(yàn),在成果中加入尺長改正改正方法

三、外界環(huán)境的影響:

誤差儀器下沉和水準(zhǔn)尺下沉的誤差點(diǎn)地球曲率和大氣折光的誤差0.3m氣候的影響

最好選擇無風(fēng)的陰天,若是晴天應(yīng)打傘保護(hù)儀器前后視距相等,控制視線離地面距離不低于改正方法將腳架踩實(shí)、選擇堅(jiān)實(shí)的地點(diǎn)安置儀器和轉(zhuǎn)

第二部分線路施工測量

2.1、實(shí)習(xí)目的

熟悉全站儀的操作方法掌握極坐標(biāo)法測設(shè)點(diǎn)位的方法

掌握圓曲線加緩和曲線點(diǎn)位坐標(biāo)計(jì)算方法

2.2、儀器設(shè)備

每組領(lǐng)取全站儀一套、單棱鏡一把、木樁若干、錘一把。

2.3、實(shí)訓(xùn)任務(wù)

某高速公路JD6曲線設(shè)計(jì)資料如下:R=500m,l0=30m,α

=1020′30",JD6里程為DK3+2**(**后兩位學(xué)號).253。

1、要求按組號置鏡于看臺(tái)的控制樁點(diǎn)(測站間距8米,主席臺(tái)上2個(gè)測站,南北兩側(cè)各4個(gè)測站,測站編號由北向南依次編號),將操場內(nèi)旗桿方向作為后視方向(方位角由已知坐標(biāo)計(jì)算),測設(shè)整條曲線。

2、測設(shè)曲線邊樁,要求左側(cè)2米,右側(cè)2米。3、編寫實(shí)訓(xùn)總結(jié)

控制點(diǎn)資料匯總表

測站編號12345678910后視旗桿測站坐標(biāo)Y=571.2208X=561.1654Y=575.1094X=554.1740Y=578.9980X=547.1827Y=582.8866X=540.1914Y=590.6638X=526.2087Y=594.5524X=519.2173Y=600.3648X=508.6367Y=604.4435X=501.6854Y=608.2022X=494.6762Y=612.0866X=487.6923Y=509.0962X=475.8527ZD1坐標(biāo)交點(diǎn)坐標(biāo)Y=540.2982X=577.3670Y=566.4394X=507.8295Y=534.7233X=574.5178Y=560.8646X=504.9803Y=529.1485X=571.6687Y=555.2898X=502.1312Y=523.5737X=568.8195Y=549.7150X=499.2820Y=517.9989X=565.9704Y=544.1402X=496.4328Y=512.4241X=563.1212Y=538.5653X=493.5837Y=506.8492X=560.2721Y=532.9905X=490.7345Y=501.2744X=557.4229Y=527.4157X=487.8854Y=495.6996X=554.5737Y=521.3959X=484.8088Y=489.5502X=551.7246Y=516.2661X=482.1871全站儀放樣時(shí)請計(jì)算測站到旗桿方位角,用方位角控制后視方向

2.4、數(shù)據(jù)計(jì)算

已知R=500m,l0=30m,α

=1020′30",JD6里程為DK3+248.253。ZD1坐標(biāo)

(560.2721,506.8492),交點(diǎn)坐標(biāo)(490.7345,532,9905),左右邊樁各2m。(緩和曲線每10m加樁,圓曲線每20m加樁)解:⑴曲線要素:

緩和曲線切線角=

l。180=1°43′7.94″2Rπ3l。l切垂距m=-=14.9996m22240R圓曲線內(nèi)移距p=l。224R=0.075m

α2切線長T=m+(R+p)×tan=60.253m

πRα180曲線長L2l。πR(α2β0)180l。=120.248m

外失距E0(Rp)sec2R=2.118m

切曲差q2TL=2×60.253-120.248=0.258m

⑵主點(diǎn)里程計(jì)算:JD6里程DK3+248.253-T)60.253

ZH里程DK3+187.999

+l0)30.000HY里程DK3+217.999

L2l0+

2)30.124

QZ里程DK3+248.123

L2l0+

2)30.124

YH里程DK3+278.247

+l0)30.000HZ里程DK3+308.247

檢核:HZ里程=ZH里程+2*T-q

即DK3+270.248=DK3+210.253+2*60.253-0.258

∴計(jì)算正確

⑶HZ點(diǎn)坐標(biāo)計(jì)算:

XHZXJD6Tcos30°56′40″=532.9905-60.254cos30°56′40″=439.057YHZYJD6Tsin30°56′40″=490.7346+60.254sin30°56′40″=563.974

⑸中線點(diǎn)計(jì)算:

ZHJD6=(532.9905-506.8492)/(490.7345-560.2721)=159°23′50″

HZ~JD6ZH~JD6左+180°=329°03′20″

緩和曲線部分:

xilili52240Rl0yili36Rl

圓曲線部分:

xi=Rsinαi+myi=R(1cosαi)+p(ilil。1800)Rπ坐標(biāo)轉(zhuǎn)換公式:

ΔxnewΔxoldcosΔyoldsinxnewx原點(diǎn)xnewΔynewΔxoldsinΔyoldcos

ynewy原點(diǎn)ynew

.ZH點(diǎn)坐標(biāo)計(jì)算:

ZH點(diǎn)里程:DK3+187.999

XTcosZHYTsinZH~JD660.253cos159°23′50″=-56.399460.253sin159°23′50″=21.2022

~JD6②.以ZH點(diǎn)為坐標(biāo)原點(diǎn)建立坐便標(biāo)進(jìn)行計(jì)算:

1=360°-159°23′50″=200°36′10″XZH=XJD6-X=490.7345+56.3994=547.135

YZH=YJD6-Y=520.9905-21.2022=511.788

P1點(diǎn)里程:DK3+187.999li=10.000

X=X自=10.000Y=Y自=-0.0111

X施=547.135+10cos200°36′10″-0.0111sin200°36′10″=537.778

Y施=511.788-0.011cos200°36′10″-10sin200°36′10″=515.317

P2點(diǎn)里程:DK3+197.999li=20.000

X=X自=20Y=Y自=-0.089

X施=547.135+20.000cos200°36′10″-0.0889sin200°36′10″=528.446Y施=511.788-0.089cos200°36′10″-19.9996sin200°36′10″=518.909

HY點(diǎn)里程:DK3+207.999li=30.000

X=X自=29.997Y=Y自=-0.300

X施=547.135+29.997cos200°36′10″-0.300sin200°36′10″=519.162Y施=511.788-0.300cos200°36′10″-29.997sin200°36′10″=522.625

P3點(diǎn)里程:DK3+220.000li=49.001

+1°43′7.94″=3°26′16.3″

X=X自=500sin4°0′38.53″+14.99955=44.981Y=Y自=5001-cos4°0′38.53″+0.075=-1.014

X施=547.135+49.971cos200°36′10″-1.299sin200°36′10″=519.162Y施=511.788-1.299cos200°36′10″-49.971sin200°36′10″=522.388

QZ點(diǎn)里程:DK3+248..123li=60.124

30.124500180oi+1°43′7.94″=5°10′14.98″°

X=X自=500sin5°10′14.98″+14.9996=60.063Y=Y自=5001-cos5°10′14.98″+0.075=-2.110

X施=547.135+60.063cos200°36′10″-2.110sin200°36′10″=491.656Y施=511.788-2.110cos200°36′10″-60.063sin200°36′10″=534.898

③HZ點(diǎn)坐標(biāo)計(jì)算:緩和曲線部分

2=360°-329°3′20″=30°56′40″

XHZ=XJD6Tcos2=490.7345-60.254cos30°56′40″=439.057YHZ=YJD6Tsin2=532.9905+60.254sin30°56′40″=563.974

以HZ點(diǎn)為坐標(biāo)原點(diǎn)建立坐便標(biāo)進(jìn)行計(jì)算:

P"1點(diǎn)里程:DK3+298.247li=10.000

X=X自=10.000Y=Y自=0.011

X施=439.057+10.000cos30°56′40″+0.011sin30°56′40″=447.639Y施=563.974+0.011cos30°56′40″-10.000sin30°56′40″=558.841

P"2點(diǎn)里程:DK3+288.247li=20.000

X=X自=20.000Y=Y自=0.089

X施=439.057+20.000cos30°56′40″+0.089sin30°56′40″=456.256Y施=563.974+0.089cos30°56′40″-20.000sin30°56′40″=553.766

YH點(diǎn)里程:DK3+278.247li=30.000

X=X自=29.9973Y=Y自=0.300

X施=439.057+29.997cos30°56′40″+0.300sin30°56′40″=464.939Y施=563.974+0.300cos30°56′40″-29.997sin30°56′40″=548.807

P"3點(diǎn)里程:DK3+260.000li=31.248

0.248180+1°43′7.94″=1°44′50.25″i500X=X自=500sin1°44′50.25″+14.9996=31.244Y=Y自=5001-cos1°44′50.25″+0.075=0.339

X施=439.057+30.245cos30°56′40″+0.307sin30°56′40″=480.665Y施=563.974+0.307cos30°56′40″-32.245sin30°56′40″=539.594

p"4點(diǎn)里程:DK3+240.000li=51.247

30.248180+1°43′7.94″=4°2′20.84″i500X=X自=500sin4°2′20.84″+14.99955=51.215Y=Y自=500(1-cos4°2′20.84″)+0.075=1.388

X施=439.057+50.218cos30°56′40″+1.317sin30°56′40″=498.375Y施=563.974+1.317cos30°56′40″-50.218sin30°56′40″=530.386

QZ點(diǎn)里程:DK3+248.123li=60.12430.124180i500+1°43′7.94″=5°10′14.98″

X=X自=500sin5°10′14.98″+15.000=60.063Y=Y自=5001-cos5°10′14.98″+0.075=2.110

X施=439.057+60.063cos30°56′40″+2.110sin30°56′40″=491.656Y施=563.974+2.110cos30°56′40″-60.063sin30°56′40″=534.898

⑹邊樁坐標(biāo)計(jì)算:ZH→QZ部分邊樁計(jì)算緩和曲線:

x邊x中cosl

y邊y中sinl(其中l(wèi)=2m)

左=ZH~JD6-i-90°右=ZH~JD6-i+90ii22R01800

圓曲線:左=ZHx邊x中cosl

y邊y中sinl(其中l(wèi)=2m)

lil。180°+β0Rπ-i-90°右=ZH~JD6-i+90°αi=~JD6ZH點(diǎn)里程:DK3+187.999li=0.000i=0左=69°23′50″右=249°23′50″

(546.437,509.916)

(547.839,513.660)

P1點(diǎn)里程:DK3+197.999li=10.000i=0°11′27.55″

左=69°12′22.4″右=249°12′22.4″

(537.080,513.443)(538.476,517.191)

P2點(diǎn)里程:DK3+207.999li=20.000i=0°45′50.2″

左=65°46′6.1″右=248°37′59.8″527.767,517.082529.125,520.790HY點(diǎn)里程:DK3+217.999li=30.000i=1°43′7.94″左=69°40′42.1″右=246°40′42.1″

518.515,520.733519.809,524.517

P3點(diǎn)里程:DK3+220.000li=50

i20500180+1°43′7.94″=4°0′38.53″

左=56°23′11.4″右=245°23′11.4″

(516.672,521.493518.008,525.263QZ點(diǎn)里程:DK3+248.123li=30.124i=5°10′14.98″左=64°13′35″右=244°13′35″

491.124,532.970492.188,536.826

HZ→QZ部分邊樁計(jì)算緩和曲線:

x邊x中cosl

y邊y中sinl(其中l(wèi)=2m)i2左=HZ~QZ+i+90°右=HZ~QZ+i-90°ix邊x中cosly邊y中sinl2R01800

圓曲線:(其中l(wèi)=2m)

lil。180°+β0Rπ左=HZ~QZ+i+90°右=HZ~QZ+i-90°αi=HZ里程:DK3+308.247li=0.000i=0

左=59°03′20″右=239°03′20″

438.124,562.102439.761,565.846

P"1點(diǎn)里程:DK3+298.247li=10.000i=0°11′27.55″

左=59°14′47.5″右=239°14′47.5″

446.998,556,967448.337,560.715

P"2點(diǎn)里程:DK3+288.247li=20.000i=0°45′50.2″

左=59°49′10.2″右=239°49′10.2″

455.634,551.885456.935,555.647YH點(diǎn)里程:DK3+278.247li=30.000i=1°43′7.94″左=60°46′27.9″右=240°46′27.9″

464.349,546.915465.586,550.699

P"3點(diǎn)里程:DK3+260.000li=30.248i=1°44′50.25″

左=240°46′27.9″右=60°46′27.9″

(480.018,536.701481.313,541.486

p"4點(diǎn)里程:DK3+240.000li=50.248i=4°2′20.84″

左=243°5′40.84″右=63°5′40.84″

497.874,528.449498.876,532.322

QZ點(diǎn)里程:DK3+231.124li=30.124i=5°10′14.98″左=64°13′35″右=244°13′35″

491.124,532.970492.188,536.826

以上計(jì)算結(jié)果如下表所示:

線路邊樁坐標(biāo)線路中樁坐標(biāo)線路右邊樁坐標(biāo)線路左邊樁坐標(biāo)X(ZH)DK3+187.999DK3+197.999DK3+207.999DK3+220.000YXYXY547.135511.788547.839513.660546.431509.916537.778515.317538.476517.191537.080513.443528.446518.909529.125520.790527.767517.028517.312523.388518.008525.263516.672521.493HYDK3+217.999519.162522.625519.809524.517518.515520.733DK3+240.000498.996531.416499.616533.317498.432529.497QZDK3+248.123491.566534.898492.188536.825491.124532.970DK3+240.000DK3+260.000DK3+288.247DK3+298.247483.696538.829498.876532.322497.874528.449466.028548.199481.313541.486480.018537.701456.256553.766456.935555.647455.634551.885447.639558.841448.337560.715446.998556.967YHDK3+278.247464.939548.807465.586550.699464.349546.915HZDK3+308.247439.057563.974439.761565.846438.124562.102

2.5、測量方法

全站儀放樣法

2.6、誤差以及誤差分析

(一)、主觀原因:

1、數(shù)據(jù)計(jì)算有誤導(dǎo)致放樣曲線不符合要求;2、輸入數(shù)據(jù)時(shí)人為疏忽輸入錯(cuò)誤數(shù)據(jù);3、對儀器的精度保留要求不同造成的誤差;

4、扶棱鏡的同學(xué)棱鏡沒有正對全站儀使得掃描數(shù)據(jù)有誤,導(dǎo)致定出樁位與原正確樁位不符;

5、定樁人員的疏忽,導(dǎo)致定出錯(cuò)誤樁位(二)、客觀原因:

1、儀器有誤造成的不必要誤差;2、氣候的影響

第三部分橋梁施工測量

3.1、實(shí)習(xí)目的

1、掌握橋梁墩臺(tái)坐標(biāo)計(jì)算方法;2、掌握橋梁基礎(chǔ)樁位坐標(biāo)計(jì)算的方法

3、掌握利用全站儀進(jìn)行曲線橋梁樁基和承臺(tái)放樣的方法

3.2、儀器設(shè)備

每組領(lǐng)取全站儀一套、單棱鏡一把、木樁若干、錘一把。

3.3、實(shí)訓(xùn)任務(wù)

1、計(jì)算曲線橋的墩臺(tái)對應(yīng)線路中線坐標(biāo);

2、根據(jù)設(shè)計(jì)資料計(jì)算1#墩、2#墩、3#墩中心坐標(biāo),并放樣;3、根據(jù)設(shè)計(jì)圖紙,計(jì)算樁基中心坐標(biāo),并放樣;4、根據(jù)設(shè)計(jì)圖紙,計(jì)算承臺(tái)四角的坐標(biāo),并放樣;5、編寫實(shí)訓(xùn)總結(jié)

R=500mα=34°45′00″l0=80mT=196.61mL=383.25mZHDK67+833.73HYDK67+913.73

3.4、曲線數(shù)據(jù)計(jì)算

解:1.選定

:

根據(jù)橋位特點(diǎn),選定HZ為坐標(biāo)原點(diǎn),HZ至JD的切線為X軸的正方向。2.計(jì)算

(1)求緩和曲線函數(shù)查表或計(jì)算得m=

l02l032240R=

802803224050039.992m

80p=l00.533m

24R2450080180l。180===4°35′1.18″25002Rπ22(2)求l及角(緩和曲線上墩臺(tái))

90(71.16)2l3=71.16mRl033735.91

l4胸=46.34m4胸=1°32′16.65″l4尾=40.79m4尾=1°11′29.85″

(3)求S及角(圓曲線上墩臺(tái))s2=23.98m2=2°44′52.46″s1=56.80m1=6°30′31.68″

s0胸=81.66m0胸=9°21′27.17″

s0尾=89.71m0尾=10°16′48.0″

(4)坐標(biāo)計(jì)算緩和曲線:X"Al-l52240Rl0Y"Al36Rl0"l733336Rl0

XA=XA+EsinYA=YAEcos

"3"X=71.16-

71.162524050080=71.131

Y=

"371.163650080-

71.1637333650080=-1.501

X3=71.131+0.12sin3°37′35.91″=71.139Y3=1.501+0.12cos3°37′35.91″=-1.381

X‘4胸墻=46.34-

46.34252336500803=46.337

Y"4胸墻=

46.34650080-46.3473333650080=-0.415

X4胸墻=46.337+0.04sin1°32′16.65″=46.338Y4胸墻=-0.415+0.04cos1°32′16.65″=-0.375

X"4臺(tái)尾=40.79-

40.7952240500803=40.788

Y"4臺(tái)尾=

40.79650080-40.7973333650080=-0.283

X4臺(tái)尾=40.788+0.04sin1°11′29.85″=40.789Y4臺(tái)尾=-0.283+0.04cos1°11′29.85″=-0.243

圓曲線:XA=Rsin(0+)+mYA=(R+P)-Rcos(0+)

xAxAEsin(m)YAYAEcos(m)

X2=500sin4°35′1.18″+2°44′52.46″+39.992=103.798Y2=555.533-500cos4°35′1.18″+2°44′52.46″=-4.621

""""http://X2=103.798+0.13sin4°35′1.18″+2°44′52.46″=103.815

X1=500sin4°35′1.18″+6°30′31.68″+39.992=136.188Y1=555.533-500cos4°35′1.18″+6°30′31.68″=-9.874

""X1=136.188+0.13sin4°35′1.18″+6°30′31.68″=136.213Y1=-9.874+0.13cos4°35′1.18″+6°30′31.68″=-9.74

X0胸墻=500sin4°35′1.18″+9°21′27.17″+39.992=160.455Y0胸墻==555.533-500cos4°35′1.18″+9°21′27.17″=-15.261

""X0胸墻=160.455+0.08sin4°35′1.18″+9°21′27.17″=160.474Y0胸墻=-15.262+0.08cos4°35′1.18″+9°21′27.17″=-15.183X0臺(tái)尾=500sin4°35′1.18″+10°16′48.0″+39.992=168.252Y0臺(tái)尾==555.533-500cos4°35′1.18″+10°16′48.0″=-17.264

""X0臺(tái)尾168.252+0.08sin4°35′1.18″+10°16′48.0″=168.273Y0臺(tái)尾=-17.264+0.08cos4°35′1.18″+10°16′48.0″=-17.187

上述計(jì)算結(jié)果綜合如下表3.1和3.2。

表3.1緩和曲線上墩臺(tái)橋梁工作線交點(diǎn)坐標(biāo)計(jì)算表

xAxAEsin(m)/x(m)/AE(m)β墩臺(tái)號y(m)/AYAYAEcos(m)/備注N3墩71.131-1.50146.337-0.41540.788-0.2830.123°37"35.91"1°32"16.65"1°11"29.85"71.139-1.381第四象限y為負(fù)N4臺(tái)胸墻N4臺(tái)尾

0.040.0446.338-0.37540.789-0.243表3.2圓曲線上墩臺(tái)橋梁工作線交點(diǎn)坐標(biāo)計(jì)算表

xA(m)/xAxEsin(0)A墩臺(tái)號yA(m)/EθYAyEcos(0)A備注N2墩N1墩N0臺(tái)胸墻N0臺(tái)尾103.798-4.621136.188-9.874160.455-15.261168.2520.130.130.080.082°44"52.46"6°30"31.68"9°21"27.18"10°16"48.0"23

103.815-4.492136.213-9.746160.474-15.183168.273第四象限y為負(fù)

-17.264-17.1870=

R=500mP=0.5333mβ(5)Q點(diǎn)坐標(biāo)計(jì)算

4°35"1.18"m=39.992

如圖所示,將置鏡點(diǎn)選擇在Q點(diǎn)。線路貫通測量時(shí),已測定ZD3到HZ點(diǎn)的距離S1=23.768m。置鏡點(diǎn)在ZD3測得∠θ=17°51"39",并測得ZD3至Q點(diǎn)的距離S2=98.835m。Q點(diǎn)的坐標(biāo)計(jì)算如下:

θZD3HZSiQYHxy

x98.835cos10821-23.768=75.047y-98.853sin1°08′21″=-1.965

(6)橋梁墩臺(tái)放樣數(shù)據(jù)計(jì)算

數(shù)據(jù)計(jì)算見表3.3,前視方位角的象限應(yīng)按x及y的符號確定。測設(shè)角β始終用前視方位角減后視方位角,不夠減時(shí)加360°。這樣算出的是順撥角度。

公式:xn~n1xn1xnyn~n1yn1ynSn~n1yn~n1an~n1arctanxn~n1an~n1an~n1xn~n1yn~n1

22計(jì)算過程:XQ~0臺(tái)尾=X0臺(tái)尾-XQ=168.273-75.047=93.226

YQ~0臺(tái)尾=Y0臺(tái)尾-YQ=-17.187--1.965=-15.222SQ~0臺(tái)尾=

93.2262(-15.222)=94.461

2

Q~0臺(tái)尾=arctan(

-15.22293.226)=-9°16′24.45″

-9°16′24.45″+360°=350°43′35.75″

=Q~0臺(tái)尾-Q~ZD3=350°43′35.75″-178°51′39.0″=171°51′56.75″

XQ~0胸墻=160.474-75.047=85.427

YQ~0胸墻=-15.183--1.965=-13.218SQ~0胸墻=85.4272(-13.218)=86.444

2Q~0胸墻=arctan(

-13.21885.427)=-8°47′43.97″

-8°47′43.97″+360°=351°12′16.03″

=351°12′16.03″-178°51′39.0″=172°20′37.03″

XQ~1=136.213-75.047=61.166YQ~1=-9.746-(-1.965)=-7.781SQ~1=

61.1662(-7.781)=61.659

2Q~1=arctan(

-7.78161.166)=-7°14′59.01″-7°14′59.01″+360°=352°45′0.99″

=352°45′0.99″-178°51′39.0″=173°53′21.99″

XQ~2=103.815-75.047=28.768YQ~2=-4.492-(-1.965)=-2.527SQ~2=

28.768(-2.527)=28.879

22Q~2=arctan(

-2.52728.768)=-5°1′12.05″-5°1′12.05″+360°=354°58′47.95″

=354°58′47.95″-178°51′39.0″=176°7′8.95″

XQ~3=71.139-75.047=-3.908YQ~3=-1.381--1.965=0.584SQ~3=

(3.908)0.58422=3.951

Q~3=arctan

0.5843.908=-8°29′57.19″+180°=171°30′2.81″

=171°30′2.81″-178°51′39.0″=-7°21′36.19″

XQ~4胸墻=46.338-75.047=-28.709YQ~4胸墻=-0.375--1.965=1.590SQ~4胸墻=

-28.70921.59021.59028.70928.753

Q~4胸墻arctan-3°10′11.97″+180°=176°49′48.03″

=176°49′48.03″-178°51′39.0″=-2°1′50.97″+360°=357°58′9.03″

XQ~4臺(tái)尾40.789-75.047=-34.258YQ~4臺(tái)尾=-0.243--1.965=1.722SQ~4臺(tái)尾=

-34.25821.72221.722-34.258=34.301

Q~4臺(tái)尾=arctan

=-2°52′39.31″=180°=177°07′20.69″

=177°07′20.69″-178°51′39.0″=-1°44′18.31″+360°=358°15′41.69″

表3.3橋梁墩臺(tái)放樣數(shù)據(jù)計(jì)算表置鏡點(diǎn)(n)名稱QX=75.0475(m)YN=1.9649(m)N后視點(diǎn)(n-1)名稱:ZD3Xn-1=-23.7680(m)Yn-1=0后視方位角αn-n1=178°51"39".0測設(shè)點(diǎn)(n+1)名稱xn1N0臺(tái)尾N0臺(tái)胸墻N1墩N2墩N3墩N4臺(tái)胸墻N4臺(tái)尾168.273160.474136.213103.81571.13946.33840.789yn1-17.187-15.183-9.746-4.492-1.381-0.375-0.243xn~n193.22685.42761.16628.768-3.908-28.709-34.258yn~n1-15.222-13.218-7.781-2.527+0.584+1.59+1.722測設(shè)邊長Sn~n194.461350°43"35.75"171°51"56.75"86.44461.65928.8793.95128.75334.301前視方位角n~n1351°12"352°45"354°58"171°30"176°49"177°07"16.03"0.99"47.95"2.81″48.03"20.69"測設(shè)角β172°20"173°53"176°07"352°38"357°58"358°15"37.03"21.99"8.95"23.81"9.03"41.69"(7)橋梁工作線交點(diǎn)距及偏角復(fù)核:計(jì)算見表3.4。計(jì)算公式:

XXYSi1X1

Yi1Y1X2YY2

TarctanX

Ti1Ti

計(jì)算過程:

X0臺(tái)尾~胸墻=160.474-168.273=-7.799Y0臺(tái)尾~胸墻=-15.183-(-17.187)=2.004

S=(7.799)22.004T=arctan

2.004-7.7992=8.052

=--14°24′38.63″+180°=165°35′21.37″

X0胸墻~1=136.213-160.474=-24.261Y0胸墻~1=-9.746-(-15.183)=+5.437

S=(24.261)25.437T=arctan

5.43724.2612=24.863

=-12°37′55.36″+180°=167°22′04.64″

0胸墻=167°22′04.64″-165°35′21.37″=1°46′43.27″X1~2=103.815-136.213=-32.398Y1~2=-4.492-(-9.746)=+5.254

S=(32,398)5.254T=arctan

5.25432.39822=32.821

=-09°12′41.4″+180°=170°47′18.6″

1=170°47′18.6″-167°22′04.64″=3°25′13.99″

X2~3=71.139-103.815=-32.676

Y2~3=-1.381-(-4.492)=+3.111

S=(32.676)3.111T=arctan

22=32.824

3.11132.676=-5°26′19″+180°=174°33′41″

2=174°33′41″-170°47′18.6″=3°46′22.4″

X3~4胸墻=46.338-71.139=-24.801Y3~4胸墻=-0.375-(-1.381)=+1.006

S=

(24.801)1.00622=24.821

T=arctan

1.00624.801=-2°19′22.2″+180°=177°40′37.8″

3=177°40′37.8″-174°33′41″=3°06′56.8″

X4胸墻~臺(tái)尾=40.789-46.338=-5.549Y4胸墻~臺(tái)尾=-0.243-(-0.375)=+0.132

S=(5.549)20.132T=arctan

0.1325.5492=5.551

=-1°11′45.8″+180°=178°38′14.2″

4胸墻=178-°38′14.2″-177°40′37.8″=0°57′36.4″

表3.4橋梁工作線交點(diǎn)距及偏角復(fù)核計(jì)算表坐標(biāo)點(diǎn)名XY坐標(biāo)增量工作線△X(m)-7.799160.474-15.183-24.261136.213103.81571.139-9.746-32.398N2墩N3墩N4臺(tái)胸墻N4臺(tái)尾-4.492-32.676-1.381-24.80146.338-0.375-5.54940.789-0.243+0.1325.5511783814.2+1.00624.8211774037.8+3.11132.8241743341+5.25432.8211704718.6+5.43724.863△Y(m)+2.004交點(diǎn)距S(m)8.052工作線方位角T°""1653521.371672204.64工作線偏角iN0臺(tái)尾N0臺(tái)胸墻N1墩168.273-17.187°""14643.2732513.9934622.430656.805736.4

某橋梁設(shè)計(jì)平面圖如上,

左側(cè)為1#墩、2#墩、3#墩的基礎(chǔ)平面圖,請根據(jù)設(shè)計(jì)圖紙完成相應(yīng)測量工作。

3.5、墩臺(tái)數(shù)據(jù)計(jì)算

1#墩

中心坐標(biāo)(136.213,-9.746)

=6°30′31.68″

承臺(tái)四角自定義坐標(biāo):X1=Y1=

3.125.252

=1.55X2=-1.55X3=-1.55X4=1.55=2.625Y2=2.625Y3=-2.625Y4=-2.625

承臺(tái)四角施工坐標(biāo):

X1=136.213+1.55cos6°30′31.68″+2.625sin6°30′31.68″=138.051Y1=-9.746-1.55sin6°30′31.68″+2.625cos6°30′31.68″=-7.314

""X2Y2""=136.213-1.55cos6°30′31.68″+2.625sin6°30′31.68″=134.971

=-9.746+1.55sin6°30′31.68″+2.625cos6°30′31.68″=-6.962

"X3Y3"=136.213-1.55cos6°30′31.68″-2.625sin6°30′31.6″=134.375

=-9.746+1.55sin6°30′31.68″-2.625cos6°30′31.68″=-12.178

"X4=136.213+1.55cos6°30′31.68″-2.625sin6°30′31.68″=137.455Y4=-9.746-1.55sin6°30′31.68″-2.625cos6°30′31.68″=-12.530

"2#墩

中心坐標(biāo)(103.815,-4.492)

=2°44′52.46″

承臺(tái)四角自定義坐標(biāo):X1=Y1=

3.125.252=1.55X2=-1.55X3=-1.55X4=1.55=2.625Y2=2.625Y3=-2.625Y4=-2.625

承臺(tái)四角施工坐標(biāo):

X1=103.815+1.55cos2°4′52.46″+2.625sin2°44′52.46″=105.489Y1=-4.492-1.55sin2°44′52.46″+2.625cos2°4′52.46″=-1.944

""X2=103.815-1.55cos2°4′52.46″+2.625sin2°44′52.46″=102.393Y2=-4.492+1.55sin2°44′52.46″+2.625cos2°4′52.46″=-1.796

""X3=103.815-1.55cos2°4′52.46″-2.625sin2°44′52.46″=102.141Y3=-4.492+1.55sin2°44′52.46″-2.625cos2°4′52.46″=-7.040

X4=103.815+1.55cos2°4′52.46″-2.625sin2°44′52.46″=105.237Y4=-4.492-1.55sin2°44′52.46″-2.625cos2°4′52.46″=-7.188

""""3#墩

中心坐標(biāo)(71.139,-1.381)=6°37′35.91″

承臺(tái)四角自定義坐標(biāo):

3.1X1XXX=2=1.552=-1.553=-1.554=1.55

5.25Y1=2=2.625

Y2=2.625

Y3=-2.625

Y4=-2.625

承臺(tái)四角施工坐標(biāo):

X1Y1""=71.139+1.55cos6°37′35.91″+2.625sin6°37′35.91″=72.852

=-1.381-1.55sin6°37′35.91″+2.625cos6°37′35.91″=1.141

"X2=71.139-1.55cos6°37′35.91″+2.625sin6°37′35.91″=69.758Y2=-1.381+1.55sin6°37′35.91″+2.625cos6°37′35.91″1.337

32

"

X3=71.139-1.55cos6°37′35.91″-2.625sin6°37′35.91″=69.426Y3=-1.381+1.55sin6°37′35.91″-2.625cos6°37′35.91″-3.903

X4=71.139+1.55cos6°37′35.91″-2.625sin6°37′35.91″=72.520Y4=-1.381-1.55sin6°37′35.91″-2.625cos6°37′35.91″=-4.099

""""3.6、測量方法

全站儀放樣法

參考文獻(xiàn)

王兆祥主編.鐵道工程測量.北京:中國鐵道出版社,201*

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