结构力学弯矩图百题练习答案.pdf

静定结构弯矩图百题练习答案 2 2 qL 8 qL 2 2 2 qL qL 2 4 8 2 qL 2 qL 8 PL 4 2 qL 2 qL /8 L q M=qL 2 L/2 L L P 2PL PL L q L P=2qL P L L P L q L L L P 2P L L L L q L L M P=qL L q L L 2P M=PL P=qL L q L q L P=qL M=qL 2 L q L q L q L/4 L/4 L/2 一、梁 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) 2PL 9qL 2 2 PL 3 4pL 5pL 3 qL 2 2 M 2 qL 2 qL 2 2 + pL pL 2 2 qL 2 2 5qL 3qL 2 2 2 2 qL qL 2 8 8 2 qL 5qL 2 32 32 2 5qL 8 qL 2 1qa 2 2 3qa 2 2 8 2 qa 8 2 9qa PL 2 2 3PL 3PL 3PL 2 PL 2 2 PL PL 2m q=10 60 15 2m 2m 2m a 2a a q M=2qa 3a a2 a2 aaa2 a 4 a q q P=2qa P=qa M=qa 2 L M=PL L P 30 0 L/2 L/2 L/2 L/2 L L P P (16) (17) (18) 二、悬臂式刚架 (19) (20) (21) 30 55 5 20 2 2 qa PL 2 PL 2 2qa 4qa 2 2 8qa 16qa 2 15qa 2 17qa 2 2 q L (22) 2 2 qL 2 3 qa 2 qa 2 2 2 2 qa 2 2 qa 2 qa 3PL 2PL PL 3PL Pa Pa (28) (27) (26) (25) (24) (23) q q 2a aa a/2 q qa qa a/2 a q qa a a 2PL P L 2L LL L P 2L LL P P a a a 2Pa qa /8 2 2 qa /2 qa 2 2 qa 2 qa 2 qa /8 2 qa PL 2 4 2 2 qa qa 2 2 2 qa 2cos 2 qL 2 + 2 qL 2 2cos qL 2 qL 2 2 2 2 qL 90 90 100 80 60 100 100 Pa Pa 2m 2m 2m (34) (33) (32) (31) (30) (29) q qa a a a a L q L L/2 L/2 q L 3m 30kN 20kN/m 3m 3m 3m 40kN 10kN/m P=40kN 2m 2m 2m a P a a 5 4 15qa 2 21qa 2 8 2 2 qa 2 2 qa qa 2 qa 2 2 qa 2qa 2 PL PL Pa 2 2 Pa 2Pa Pa (40) (39) (38) (37) L (36) (35) 三、简支式刚架 a a q q 2a qa 2 a 2 qa a 2 qa q a a q q/2 a/2 qa a a a/2 P L P P a a a/2 a 2 Pa 2 Pa qa 2 2 7qa 4 6 (46) 2.595q 7qL 2 4 qL 2 4 2 2 3qL 345 45 390 480 690 690 4Pa 3 3 4Pa 4Pa 2 qa 2 2 5qa qa 2 2 qa 2 2 qa 2 2 (45) (44) (43) (42) (41) 3m 4m 4m q qL q L L L 40kN 10kN/m 3m 3m 3m 3m 3m 4Pa a a a2 a qa q a a 2a 2 M=qa q a/2 a/2 a 3qa 2 2 PL PL 2 qL qL 2 2 (48) (47) P P L 2L L q L L 8 5qa 2 2 qa 8 2 qa 8 8 qa 2 2 qa 8 q q q 8 qa 2 2 5qa 8 q q (49) 7P M M 2 Pa 8 2 P P 2 无弯矩 N=P/2 2 2qL 2qL 2 (5 (50) 2) (53) (51) a LLL L L L a a a M a a 2a P 1.5L q L M Pa 2 9 PL M M/2 M/2 M/2 25kN.m 25kN.m Pa/2 5qa/2 9qa/2 (58) (57) (56) (55) (54) L L/2 L/2 P L/2 L/2 L M L/2 q=20kN/m 50kN 50kN 0.5m 0.5m 2m 4m 4m a/2 a/2 P a/2 a/2 a 3a 3a 2a q qa 2qa Pa/2 65kN.m 25kN.m 25kN.m PL PL PL 四、三铰式刚架 10 2 2qa/3 2 qa 2 qa/2 PL (65) (64) (63) (62) (61) (60) (59) q a a a a q 1.5a a a M 1.5a a a q 1.5a a a a a 1.5a q 2a a a P L L qa/2 2 qa/2 2 2 qa/2 M M M M qa 2 qa 2 /8 M M M M /8 2 qa qa 2 /8 2qa/3 2 2qa/3 2 2 2qa/3 qa/2 2 PL 2 M M M qa M/4 3M/4 M/2 M/2 M/2 M/2 36kN.m 36kN.m 2q 2q 对称 2 3qa/8 2 qa/8 2 qa/2 100kN.m 200kN.m 300kN.m 300kN.m 3m 1.5m 1.5m (71) (70) (69) (68) (67) (66) a a a a L/2 L/2 L/2 L/2 3m 2m 3m 12kN 2m q 2q 2m 2m 2m 2m q a/2 a/2 a 2a a 1.5m 5m 3m 60kN 100kN.m qa/2 2 qa/8 2 3qa/8 2 M/2 M/2 M/2 q q 2q 2q 112 qa 2 2qa 2 qa 2 qL/2 Pa Pa/4 Pa/4 (77) (76) (75) (74) (73) (72) 五、复杂刚架 q a 2a 2a q a/2 a a a q L/2 L/2 L/2 q L L L L a a a P a P P a/2 a/2 a a Pa Pa qL/8 2 2 qL/32 2 qa/8 qa/2 2 2 qa qa 2 122 qa /8 2 qa Fpa/2 Pa a a a a Fp aa a a q qa a2 a 2a a qa q a a a a a P 2kN q=10kN/m 2m 2m 2m 2m 4m 4m (78) (79) (80) (81) (82) Fpa/2 对称 qa 2 2 2qa 2 qa/2 3qa 2 4Pa 6Pa 4P -8Pa 12kN.m 4kN.m 8kN.m 80kN.m 24kN.m 56kN.m 13Pa 4Pa Pa 2Pa 2qa 2 qa/2 2 qa/4 2 20kN.m 8kN.m (86) (85) (83) 2m 2m 2a a a a a a 2a P q a/2 a qa a a/2 10kN 1m q=4kN/m 1m 2m 2m 21.82kN.m 21.82kN.m (84) 5kN 5kN 5kN 4X3m=12m 3m 8m -3.536kN 2.27kN 2.27kN -5kN -10kN 10.61kN 2.27kN 2.27kN -5kN 10.61kN -3.536kN -10kN 14P/2 P P P/2 80kN.m P 3P 80kN.m 100kN.m 60kN.m 30kN.m 70kN.m 10kN.m 40kN.m 30kN.m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m (90) (89) (88) (87) P 2m 2m 2m 2m 1.5m 20kN/m 40kN 2m 2m 4m 4m 22 P P 2m 4m 4m 2m 10kN/m m 40kN 20kN 20kN 10kN/m 10kN/m 10kN/m 20kN.m 20kN.m 40kN.m 80kN.m 80kN.m 2P 15 16 M Pa/2 Pa/2 Pa/2 Pa/2 Pa/2 Pa/2 4P 4P PL/2 2 qL/2 2 3qL/2 (95) (94) (93) (92) (91) a a a a a a a a P a a a a a P 2m 4m 4m 2m 4m 0 30 0 30 P P L/2 L/2 L L q L L L M M M 4P 4P 4P 4P 4P PL/2 M 20kN.m 20kN.m 40kN.m 20kN.m 60kN.m 100kN.m M -2P 6P 4P 2PL 3PL PL 2Pa 2m (100) (99) (98) (97) (96) a a a a/2 a/2 a P L L L L L 10kN/m 2m m 2m 50kN 100kN 2m 2m 2m P a aa 2a a 60kNm m 60kN 10kN/m 20kN 2m 2m 2m 2m 2m M 5kN.m 5kN.m 4PL 2Pa 17