재료역학(mechanics of materials)은 공학을 전통적인 구분 방법으로 구분할 때 기계공학, 토목공학, 건축공학, 조선공학, 해양공학 그리고 항공공학과 같이 역학과 관련된 교육 프로그램이 요구되는 분야에서는 필수적인 과목이다. 대개의 교과 과정에서 2학년 과정에서 이를 거의 필수 성격으로 이수할 것을 요구하고 있다. 이는 해당 전공과 관련된 제품의 설계에 있어서 반드시 필요한 익혀야 될 지식이기 때문이다.

Pytel과 Kiusalaas이 공저한 이 책을 처음 받아 펼쳐 들고 읽어 본 소감은 이러하다. 이론적인 부분에 대한 군더더기 없는 원리에 대한 설명, 원리를 적용하는 단계적 예제들 그리고 원리의 이해와 응용력을 키워 줄 수 있는 다양한 연습문제들 게다가 컴퓨터를 이용하여 해결하는 문제들 등 원리의 이해에서부터 실제적인 문제에의 응용에 이르기까지 균형을 잃지 않고 체계적으로 다루고 있다는 것이었다. 이번 SI 판에서는 현재 길이-질량-시간의 단위로 주로 사용하는 SI 단위로 불리우는 국제 단위인 MKS (meter-kilogram-second) 시스템을 책 전체를 통틀어서 사용한 것이 이전 판과 다른 점이다.

저자 서문에서 기술한 방식대로 이 교재를 사용한다면 재료역학에서의 기본 원리를 이해하고 이를 실제적인 문제에 응용할 수 있는 능력까지 배양될 것으로 보인다. 이 책을 번역하면서 원문에 충실하고 가능한 이해하기 쉽도록 표현하려고 노력하였으나 재료역학을 필요로 하는 다양한 공학 분야에서 사용하는 용어에 다소 차이가 있을 수 있기에 어색한 부분이 많이 있어 보인다. 영어의 표현을 그대로 번역하면 오히려 이해하는 데에 어려움이 있기 때문에 때로는 원서의 내용을 의역한 부분이 다소 있을 수 있다. 많은 분량의 내용을 번역하는 과정에서 오류와 미흡한 부분이 있을 것으로 보인다. 이 책을 이용하는 여러분들의 아낌없는 질책과 조언을 바탕으로 더 유용한 책으로 보완할 계획이며, 이 책을 이용하는 모든 분들에게 작은 도움이 되기를 희망한다.

제1장

응력 1

1.1 개요 ·································································· 1

1.2 내력의 해석: 응력 ············································· 2

1.3 축 하중을 받는 봉 ············································· 4

a. 도심(축)하중 ················································ 4

b. Saint Venant의 원리 ·································· 5

c. 경사면에서의 응력 ······································ 6

d. 응력 해석의 과정 ······································· 8

1.4 전단응력 ·························································· 20

1.5 지압응력 ·························································· 21

제2장

변형률 35

2.1 개요 ································································ 35

2.2 축 방향 변형: 응력-변형률 선도 ······················ 36

a. 수직(축) 변형률 ········································· 36

b. 인장 시험 ················································· 38

c. 사용응력과 안전계수 ································ 40

2.3 축 하중을 받는 봉 ··········································· 41

2.4 일반화된 Hooke의 법칙 ··································· 52

a. 단축 하중; Poisson 비 ···························· 52

b. 다축 하중 ················································· 53

c. 전단 하중 ················································· 54

2.5 부정정 문제들 ·················································· 61

2.6 열응력 ····························································· 72

제3장

비틀림 87

3.1 개요 ································································ 87

3.2 원형축의 비틀림 ··············································· 88

a. 단순화를 위한 가정들 ····························· 88

b. 적합 조건 ················································· 89

c. 평형 조건 ················································· 90

d. 비틀림 공식 ·············································· 91

e. 동력 전달 ················································· 92

f. 부정정계 문제들 ········································ 93

3.3 박판 튜브의 비틀림 ········································ 108

3.4 사각 봉의 비틀림 ··········································· 117

제4장

보에서의 전단력과 모멘트 127

4.1 개요 ······························································ 127

4.2 지지점과 하중 ················································ 128

4.3 전단력-모멘트 방정식과 전단력-모멘트 선도 ··· 129

a. 부호 규약 ··············································· 130

b. 전단력과 굽힘 모멘트 선도를 결정하는 과정 130

4.4 전단력-모멘트 선도를 그리기 위한 면적법 ······ 144

a. 분포 하중 ··············································· 144

b. 집중 하중과 우력 ································· 148

c. 요약 ························································ 148

제5장

보 속의 응력 165

5.1 개요 ······························································ 165

5.2 굽힘응력 ························································ 166

a. 단순화 가정 ············································ 166

b. 적합 조건 ············································· 167

c. 평형 ························································ 168

d. 굽힘공식; 단면계수 ································ 169

e. 굽힘 응력을 구하는 과정 ······················· 171

5.3 경제적 단면들 ················································ 188

a. 표준 구조 형상 ······································· 189

b. 표준 형상을 선택하는 과정 ···················· 190

5.4 보에서의 전단응력 ·········································· 195

a. 굽힘 작용의 해석 ································· 195

b. 수평 전단응력 ········································ 197

c. 연직 전단응력 ········································· 199

d. 전단응력 식의 논의와 제한 ···················· 199

e. 직사각형과 넓은 플랜지 단면 ················ 200

f. 전단응력 해석을 위한 과정 ··················· 201

5.5 굽힘과 전단에 대한 설계 ································ 211

5.6 조립보에서의 조임구의 설계 ··························· 219

제6장

보의 처짐 233

6.1 개요 ······························································ 233

6.2 이중적분법 ····················································· 234

a. 탄성선의 미분방정식 ······························ 235

b. 미분방정식의 이중적분 ··························· 236

c. 이중적분을 위한 과정 ····························· 237

6.3 브라켓 함수를 이용한 이중적분 ······················· 250

6.4 모멘트-면적법 ················································ 261

a. 모멘트-면적 정리 ··································· 262

b. 부분별 굽힘 모멘트 선도 ······················· 264

c. 모멘트-면적법의 응용 ···························· 268

6.5 중첩법 ··························································· 278

제7장

부정정보 293

7.1 개요 ······························································ 293

7.2 이중적분법 ····················································· 294

7.3 브라켓 함수를 이용한 이중적분 ······················· 300

7.4 모멘트-면적법 ················································ 305

7.5 중첩의 원리 ··················································· 312

제8장

조합 하중에 의한 응력 325

8.1 개요 ······························································ 325

8.2 박벽 압력용기 ················································ 326

a. 원통형 용기 ············································ 326

b. 구형 용기 ··············································· 328

8.3 축 하중과 횡 하중의 조합 ······························ 333

8.4 한 점에서의 응력(평면응력) ···························· 343

a. 기준면 ···················································· 343

b. 한 점에서의 응력 상태 ··························· 344

c. 부호 규약과 아래 첨자 ··························· 345

8.5 평면응력의 변환 ············································· 346

a. 변환식 ···················································· 346

b. 주응력과 주평면 ··································· 347

c. 최대 면내 전단응력 ································ 349

d. 응력 변환 과정의 요약 ··························· 350

8.6 평면응력에 대한 Mohr 원 ······························· 357

a. Mohr 원의 작도 ······································ 358

b. Mohr 원의 특성 ····································· 359

c. Mohr 원의 확인 ······································ 360

8.7 절대 최대 전단응력 ········································ 367

a. 평면 응력 상태 ······································· 368

b. 일반적인 응력 상태 ································ 369

8.8 응력 변환의 조합 하중에 적용 ························ 372

8.9 변형률의 변환: 변형률에 대한 Mohr 원 ·········· 385

a. 변형률에 대한 복습 ································ 386

b. 평면 변형률의 변환식 ···························· 387

c. 변형률에 대한 Mohr 원 ·························· 389

8.10 스트레인 로젯 ················································ 394

a. 스트레인 게이지 ····································· 394

b. 스트레인 로젯 ········································ 395

c. 45°스트레인 로젯 ································· 395

d. 60°스트레인 로젯 ································· 396

8.11 전단계수와 탄성계수의 관계 ··························· 399

제9장

복합보 407

9.1 개요 ······························································ 407

9.2 복합보에 대한 굽힘공식 ·································· 408

9.3 복합보에서의 전단응력과 처짐 ························ 415

a. 전단응력 ················································· 415

b. 처짐 ························································ 416

9.4 보강된 콘크리트보 ·········································· 420

a. 탄성 해석 ··············································· 420

b. 극한 모멘트 해석 ··································· 421

제10장

기둥 433

10.1 개요 ······························································ 433

10.2 임계 하중 ······················································ 434

a. 임계 하중의 정의 ··································· 434

b. Euler의 공식 ··········································· 435

10.3 임계 하중의 고찰 ··········································· 437

10.4 중간 기둥에 대한 설계 공식 ··························· 444

a. 접선계수 이론 ········································ 444

b. AISC 기둥 규정 ······································ 445

10.5 편심 하중: 시컨트 공식 ·································· 452

a. 시컨트 공식의 유도 ································ 452

b. 시컨트 공식의 응용 ································ 454

제11장

보에 관한 추가적인 주제들 465

11.1 개요 ······························································ 465

11.2 얇은 두께의 보에서의 전단류 ·························· 466

11.3 전단 중심 ······················································ 468

11.4 비대칭 굽힘 ··················································· 478

a. 대칭 굽힘의 검토 ··································· 478

b. 대칭 단면 ··············································· 479

c. 중립축의 경사 ········································· 480

d. 비대칭 단면 ············································ 480

11.5 곡선보 ··························································· 488

a. 배경 ························································ 488

b. 적합성 ···················································· 488

c. 평형 ························································ 490

d. 곡선보 공식 ············································ 491

제12장

특별한 주제들 501

12.1 개요 ······························································ 501

12.2 에너지법 ························································ 502

a. 일과 변형 에너지 ··································· 502

b. 봉과 보의 변형 에너지 ··························· 502

c. Castigliano 정리에 의한 처짐 ················· 504

12.3 동하중 ··························································· 513

a. 가정 ························································ 514

b. 질량-스프링모델 ····································· 514

c. 탄성체 ····················································· 515

d. 레질리언스 계수: 인성 계수 ·················· 516

12.4 파손이론 ························································ 523

a. 취성 재료 ··············································· 523

b. 연성 재료 ··············································· 524

12.5 응력 집중 ······················································ 532

12.6 반복 하중 하의 피로 ······································ 539

제13장

비선형 작용 545

13.1 개요 ······························································ 545

13.2 극한 토크 ······················································ 546

13.3 극한 모멘트 ··················································· 548

13.4 잔류응력 ························································ 555

a. 하중-제하중사이클 ································· 555

b. 비틀림 ···················································· 555

c. 굽힘 ························································ 557

d. 탄성 스프링백 ········································ 557

13.5 극한해석 ························································ 563

a. 축 하중 ··················································· 564

b. 비틀림 ···················································· 564

c. 굽힘 ······················································· 565

부록 A

평면 도형의 특성에 대한 복습 575

A.1 면적의 1차 모멘트 ········································ 575

A.2 도형의 2차 모멘트 ········································· 576

a. 관성 모멘트와 관성곱 ···························· 576

b. 평행축 정리 ············································ 578

c. 관성반경 ················································· 579

d. 복합 면적법 ·········································· 580

A.3 도형의 2차 모멘트의 변환 ······························ 589

a. 관성 모멘트와 관성곱의 변환 ················ 589

b. 응력변환식과의 비교 ······························ 591

c. 주관성 모멘트와 주축 ····························· 591

d. 면적의 2차 모멘트에 대한 Mohr의 원 ···· 592

부록 B

표 601

B.1 보통 금속의 평균 물성값 ································ 602

B.2 광폭플랜지 단면의 특성(W-형상) ···················· 604

B.3 I-단면의 특성(S-형상) ···································· 610

B.4 채널 단면의 특성 ··········································· 611

B.5 등변 앵글 단면의 특성 ··································· 612

짝수 번호 문제의 답 ················································· 617

찾아보기 ·································································· 625