博士課程前期2年の課程
外国人留学生等特別選抜（令和5年10月入学）
一般選抜（令和6年4月入学）
専門科目試験問題（建築構造工学講座）
Master's Program Entrance Examination

SpeciaI Selection Program for Foreign Students (for Entry in October 2023)
Regular Program (for Entry in April 2024)
Questions (Structural Engineering for Architecture Course)◆注意事項/ Notice(1)配布物は以下の通りである。
Followmg sheets are distributed;‐問題用紙12枚（表紙を除く) / 12 of question sheets (except this cover sheet)‐解答用紙14枚/ 14 of answer sheets(2)解答用紙には、問題番号と受験番号のみを記入し、氏名を書いてはならない。受験番号のない
もの、 また、受験者の氏名の書いてある解答は無効となるので注意すること。
Write the question number of vour answer a nd vour examination identification number On the topof each answer sheet

Do NOT write vour namelf you don't fbllow the directions, youl･ answel･ willbe mvalidated.

(3)問題は全部で6問である。各問題に対し、別々の解答用紙に答えること。解答用紙は全部で14枚あるので、各問題に対して、複数の解答用紙を使用してもよい。
There are six (6) questions. Write the answer of each question on the different answer sheet(s). A set of
1 4 (14) answer sheets is given. You can use two (2) or more answer sheets fbr one question, if
necessaryb)‫اة‬- 45 ‫ي‬١(า

Quest!٥n 1

Answer the following questions regarding suspended ceilings where each member is entirely
pin-jointed. (Subtotal 45 marks)11-1 ‫؛‬:ặtẫfí^ẫS:íSL7tft،9Xf7(٠١l;íill/lg(;)íllT‫؛‬:ẵ5‫؟‬:lẻ:ti'Cv١6Г‫؟‬Г،9ЙАВ١Ư.,ADịị \/\fhbJr'/ỳ"ậ£o ‫كج№بؤةج‬٠‫ح‬٠m ๑mịL·ẠỷJะf:tύ';'ĩ:'ềòЬ๑tf:ẫ ff}‫؟‬v١fíiị)']ặ'№.l‫؛‬:-'ẤýMBDịilỀ
ýj.
Ό fA', á^ị،M٠á‫ (ق‬،il9!‫أده‬7‫ائ‬١‫)ة‬7(‫ اباحل‬Ị^T^I,:‫ا‬:‫ة‬7‫أؤئ‬The suspended ceiling with diagonal bar shown in Figure 1-1 is installed in an envirortment with a gravitational
acceleration g. The suspended members AB, CD and diagonal members AD have Young's modulus Eo andcross-section ‫ك‬0٠ The masses of the suspended and diagonal members are assumed to be negligible. Tlie ceiling slab
BD can be regarded as a rigid body witlt the mass m. Answer the following questions assuming that botit thesuspension and diagonal members are in the elastic range and sitali not buckle.

//////■//////////

////٠

fr

A

4Í

1

immig
\
(Gravtational Acce!erat!on g)

B

D
٥

3

1

(mass m)

‫ا‬

3İ

И 1.1

Figure 1-1(1)

Suspended ceiling with diagoital bar

m 1-1 CT)tl0ẻ:ễ:c^m5ậÍAB, CD, AD (7)‫ي‬4‫ةياذخاي|ا‬07،‫قمت‬1‫ا‬-‫اا‬-‫)ة<ة‬7(‫خ‬1,

fitil, 3^‫ةأاتيي‬80)7(‫ا‬،^‫غ]حل‬1<‫اا‬4‫ي‬:?AH:ItfÒ0 İ9.Ü)Detennine the axial force in members AB, CD, and AD under the conditions shown in Figure 1-1. Note thatthe center of gravity and the centroid of the ceiling plate BD shall coincide with eaclt otlier, and the tensile
force is taken as positive value. (9 marks)l－－■■■■■■■■■■'C

A

一P一一一一一

42

B

，
－

＜ー

加速度a(Accelerati｡n q) ､質量"!(m ass "I)１１

図1-2
Figure l-2’3〃

図l-1の吊り天井に加速度αが左向きに作用した状態

Acceleration" actmg toward lhe left direction on the suspendedceiling in Fig. 1 - 1(2)地震により図1-1の吊り天井に水平加速度αが左向きに作用し，図1-2のような状態になった。このときの，部材AB, CD, ADの軸力を求めなさい。ただし，天井版BDの重心と図心は一致するものとし，引張力を正とする。（9点）
Due to the earthquake, the suspendedceilmg m Figure l - l is suhjected to a horizontal accelerationq toward
the left direction, as shown m Figure l-2. Detennine the axial fbrces of members AB､CD. and AD. Note thatthe center of gravity and the centroid of the ceilmg plate BD shall comcide with each othex; and the tensile
fbrce is taken as positive. (9 marks)(3)

図1－2の状態における， 天井版BDの水平方向の変位を求めなさい。(9点）
Detennine the horizontal

displacement of dle ceilmg slab BD under the conditions shown in Figure 1 -2 (9marks)

－2－

一

一

－

A

C

4』

3

，
－

一し

加速度a(Accelerati｡n q) ､質量"!(m aSSﾉ"）

Figure l-3

１－

１１

図1-3

3』

図1-1の吊り天井に加速度αが右向きに作用した状態

Acceleration " acting toward the right direction on the suspended ceiling in Fig. 1 - 1(4)地震により図1-1の吊り天井に水平加速度αが右向きに作用し，図1-3のような状態になった。このときの，天井版BDの水平方向の変位を求めなさい。(9点）
Due to the earthquake, the suspended ceilmg in Figure l - l is suhjected to a horizontal acceleration q toward
the right direction, as shown in Figure l -3 . Detennine the horizontal displacement of the ceilmg slab BD under
the conditions shown m Figure l-3. (9 marks)

句

－． －

－－

－

－

A

C
■凸■■■■■■Ｂ■■■ＢＢＥ■１．００・ｌｌＤ９ｐｋ岳巳■Ｕ■■■９０凸ｒ■ＢＩ■■ＢＢｕＪｈ０。

I

I

4』

重力加速度g重力加速度g、(Gravitational ACCeleration g)(GravitationalACCele｢ationg）

B

，
I

＜ー一医

、

I

－

0

加速度α(Acceleration q)質識' (mass,"）
１１

ＩＬＭ■ＩＢⅡＩ

3J

図1-4
Figure l -4

吊り天井と壁の間の空隙

A gap between suspended ceiling and wall(5)吊り天井の周囲に壁が設置された状態について考える。地震により図1－4の吊り天井に作用する水平加速度がα=1.59のとき，天井が壁に衝突しないために必要な天井と壁の間の最小寸法（その寸法以下だと衝突する値）を，吊り材AB側，吊り材CD側，それぞれについて求めよ。(9点）
Considera simation where walls are installed around a suspendedceiling. The horizontal acceleration" actmg
on the suspendedceiling m Figure l-4 due to an earthquakeis assumed to be l.59. In this case, detennme themmmum distance between the ceiling and ihe wall required to prevent the ceiling hom colliding with the wall
(if less than the distance, they collide), on the AB side of the suspension and on the CD side of the suspension,respectivelyb (9 marks)‐4‐

W\2{:/ìflôfđỀểPơ)ýjơ)im^ò{'ỳò7flẾụấùl4l(DĨ\ýitỀI{:\ỵnòĩlLon^}:măr.'âxЦХо ttíl. f/<xơ)ặ^ơ)J^'/yi^sỀìE,٠ ‫ح؛‬0٠‫|يي؛تو№ الة)؛ةيجق‬،9٠?(yh^ltfòo-^tyì‫ًا^منجئة‬.١‫؛‬:‫ج؛‬۴]‫جلة‬. tbẶỀliũệiỶmv)^ntfòo.‫(ع‬(Hł75

Ques‫؛‬l٥n 2

Answer the following questions regarding the stress and defonnation of a statically indeterminate
frame subjected to a force of a inagnimde .p The Young’s !nodulus and moment of inertia of all themembers are E and /‫ ا‬respectively. Shear force is considered positive when it rotates tlte member ina clockwise direction, positive axial force is tension, downward vertical displacement is positive,
and ciocnise nodal rotation is positive. (Subtotal 75 marks)ŞîSîtliFigure 2 Plane frame

)A٠٠í
1)
?١ỉ:áB،ỷ^JS;^w،4٠V'،4*sJ:D١٠C^١‫؛‬:jb'‫؛‬tỏ^^Wc٠7c٠Mcl‫؛‬t^)J:، )15/‫(ي‬
Detemine the reaction forces Ил and Va at tlie point a and tlie reaction forces Wc-^c-and Mq at the point C.
(15(
marks

(2)

:cD-T-i4Â0ÉífĨ‫ ص‬У‫؛‬А,в,сы,،Ι ιΙιΛΙ^Ι،τ.
*١í:f'cít6ÍỂ-ầrl4'،:^l
(45(
.й

‫خ‬

Draw the bending moment, shear force, and axial force diagrams. Indicate the values at the points A, B, and cin the diagrams. The signs of the values of tlie shear and axial forces should be indicated. (45 marks)(3) BácD^i¿A^١c07Kf|١(j‫؛‬:. ệhiỀií mảỀHỉòXc (15,‫)ح‬
Determine tite rotation angle at the point B and tlte liorizontal, vertical, and rotation angle at the point A. (15marks)

5

(pf55 ,٥١)3

Question 3

3-1

Answer the following questions related to steel structures. (Subtotal 55 marks)]‫ [ة‬3-1‫؛‬:^t٥
ťy-m^tíŤ: 3 ịơ)%^ (§15WA'C) t'tiènồi٠tílíậ
А

nutmxiuiiťym ٠‫^ؤ‬٢‫؛‬١‫ة‬٠ it,

y /-h-ịUìAặỷị^ỂmỲẾị:f,/๙
;T٠ f7tl:J:(،9,11 ‫(|ل|ج‬1‫'ازؤ|لميءؤ‬0‫ا‬١٠‫)ةة‬7(<‫ا‬-‫ة‬٠ tt, ‫ة‬1‫^ل‬٠1‫ي؛ج‬1)0(‫؛‬:‫ا‬٦‫اة‬-‫الؤغ‬V)1'hòo Ỳ'/Viậlịi 205000N/mm2, Mflj: smgothòo ΙΚλ<7)]:%Ί:2λϊσ)7ΐ '/;;{Ι{(:)\:}'ί<t،t9í:ặl‫(؟‬.
{íặ a) -C-t^í^ÌếịltH
ũ4X٠ÍÌ§í‫؛‬ỶI[Ố٠Ìd3،tư7٠L/‫ ؤ غ‬،:‫جا‬arta/-300‫تخ ان‬200‫ع‬،7(‫ لؤحل‬Ж‫|ت؛‬:‫غة‬٠๙) Pni)40 ,٥(Question 3-1

Figure 3-1 shows a Steel stmcmre consisting of three pin-supported members (members A-C). The

stiffeners are provided in the center of the members, and the members are pin-connected to the stiffeners. Tlte
members do not deform out.of.plane in the ^-direction, and local deformation of the members is assumed to be
restrained by stiffeners. The cross section of tlie member is shown in Figure (c). Young's modulus is 205000 พททท2and tire steel material is SN490. On the upper side of the member, Pvo flanges are welded to a Steel plate (thicknessof a) as shown in Figure (c). The weld size is set to be the maximum from the cross section of the member and tlie
plate.

When /=300‫ ى‬and л=200й, answer the following questions. (40 marks)

WT. 0)3(‫ذ؛‬7‫ط‬١0‫؟‬٤‫الإ‬
Answer the following questions about Figure (a).

(!)^1‫؛‬๑i'μmlL·\t)fỀỲtìỷ)Xo[Цф(7)в^^^ЯП١Г ЙАЧ
Find the stress acting on members A~c using the symbols in the figure.

(2( ٠=10mmCOł^Hfl:||;^^|(7)il?łl٥6،t٥ 7،‫ةف'د‬,
biximixbl[
Find the load p at short-term allowable stress when ٥=10mm. In the calculation process, each physical quantity

may also be calculated as Pvo significant digits.
(3)

Illustrate the collapse fonn of the strucmre.

J¿i،T, mih){:/)[\XliXo
Answer the following questions about Figure (b).

(4)IĨ(7ràĨtẫrff]v١tếỉ‫؛‬WA\C(7>ítli,ù:^/.ế^l*j:
Find the stress actltig on members A-C using the symbols in the figure.

(5) «=10mm،7)ẻ‫؛‬Ề,

7 h ‫كد‬fj:ỳò, l\lỀU.[:ị^\/\XM0ÌỀI:llt(]blXl\-'^Ę-lXbX\\,
Find the bending moment M at short-term allowable sness when ٠=10mm. In tlie calculation process, eachphysical quantity may also be calculated as Pvo slgniFicantdigits.

(6) ttV|íậcDtũIfặ‫؛‬٠ũj;
Illustrate the collapse form of the stmcmre.
-6-

問題3－2

次の間に答えよ。（15点）

Qu estion 3-2

Answer the fbllowmg questions. (1 5 marks)(1) 低層鋼構造骨組の代表的な構造形式を二例以上挙げ,それぞれの耐震上の特徴の相違を簡潔に説明せよ。
List at least two typical strucmral types of low-rise steel hfames and briefly explam the differences m theirseismic characteristics.

(2) 基準強度F値はどのように定められているか，簡潔に説明せよ。

Briefly explam how the reference strength F value is detennmed.

CｧPａ(a)圧縮力

７－

鋼

α

部材cI

部材

２

訓

ゴゴ

ル

I MZEIル

胃雨羽一蔀罧5

6‘

］ａ

一し一

部材

ル

戸

補剛材

一

L，

八Ａ １

部材

����

２

y

ル

補剛材

］珈血

〃2

補剛材

６８９８０８４００１ｔ��������

似．
補剛材

I、
スティフ

６９１１１１１００８００８●

一

＝可

ー

一霊幽、〕ⅢⅢⅢ川川凹嗣Ⅲ剛門川Ⅲ川Ⅲ山

一一

I

〃2

／

一醍一

一

壼聖’
一童 ｒＩ１６６ｔ０８０００Ｉｌ上０００００００１－▼０川川畑潟』

一一｜両一

一一『

’一 一

一詰一式
一》一

一一一
1－↑‐

すみ肉溶接

(b)曲げモーメント(c)断面および接合部の詳細図3－1ピン支持された3本の部材で構成される構造体
Rigid member
言巳P －－

重憲

lllletweld

…

一

α
ａ
ワーワー

1，

コゴ

1

〃2
L－－』
3a
ノ

BmcingBmcin座

ル

ル

ル

ル

鱸鰹ユー
"………春帯(a) Compressive fbrce

弧~列
I蕊謹溌蕊

一

Membc
C

I

α［

α［

王

6口

］ａ

V

←しX

BIacing

α
〆○

↑

C、

可I

Bmcing

一

Z

rl1
一

ﾔー

〃

(b) Bending moment(c) Cross-section andJomt Details

Figure 3 -1 Steel strucmre consistmg of three pin-supported members .

-7－)ił 55 .‫(عب‬

4

Question 4

Answer the fo!lowing questions on reinforced concrete structures (Subtota! 55 marks)(40 ,٥)4-1

Quesbon 4-1 (40 marks)
I 4-1 \:^fl ‫ؤ‬،‫غا‬1|1 ẴA>Ềlj'yỉ7 ‫لا‬
Ltv١ố٥ tìc7)|®{j;| 4-2 ،/) ¿ ‫ يي‬V) .e,;‫< ي‬ïïMmϋ(:τΚ¥Ι/. ¿rq١rầf I 2Ν

I ١‫ئل‬7|،‫؛<^بي‬:‫ة(ئ^هؤلا‬Horizontal force p and vertical load 2Ν are applying to a single story - single bay reinforced concrete (RC) frameas shown in Fig. 4.1. Column section is shown in Fig. 4-2 and beams are stiff and strong enougli.
(1)

Draw bending moment diagram of columns.

У ьMuli, д\ГтШ{4-\уешп0)2( .‫الس^دةة‬M٧ = 0.8atffyDł0.5WD(l

N

bDơB

)

ttíl, b:^.ţ๑ặẵ, ٥:tt،7)fv‫جل‬:‫ت‬١,¿‫ة‬., ír®F،‫)؟‬D

(4-1)
ỳ\)

hrmiiì.

ơỵ ■.ÚÌ,Ì)ỴIỀIÌ

Explain the reason that ultimate flexural moment Wi، of a RC column can be approximated by Eq. 4-1 based on
sttess distìbution on a column section.
M= 0.8a،ơy٥ + 0.5WỮ(l

N

bDơB

)

(4-1)

Where, ٥: width of a column section, ٥: deptlt of a column section, σ٥: concrete compressive strength, ٩٠: baryielding strength.

(3) Hặừịếẹim p‫ص‬-۶3(~٠‫ج‬. łtLł^L 2
ỹ7Ỳ$l,

δ (D?ễ\ịim 4-3 Ơ)X จ ،: 3 jịnhề'cmiti:'Ề òtfòc 'ịợ)Aỹ
L/■:?-،14^‫ت‬7‫غ؟ل‬٠)7‫ئد‬9‫؛‬:‫ا‬11‫ت‬1‫<ة‬7‫ل‬
‫\لح‬
‫ؤ‬
H<Dự

riliỉfữưlJti.â,‫ؤ‬‫أ‬7‫ىقئ‬/<ỹ7h‫و‬- a)¿, b)٥, ο)σ٥, d) ٩٠, e)^.
Lateral force p - horizontal displacement ‫د‬relation is simplified by a tri-linear line as shown in Fig. 4-3. Drawp -‫ ي‬relations and explain differences of cracking and yieldiitg points when the following parameters a) to f)
become double, respectively,

parameters-

a) b,

b)٥,

c) σ٥١d) ٩٠,

e)^

0 h.

-8-

水平荷重P蕊

α’:引張主筋断面積
ぴ､.：主筋降伏強度

▲

柱

階高ル

曲げ降伏

トー→

▼

eq

蕊
●◆●

【･:･勘

■■■
■由｡

PI!

Pc,

■■

1

柱

■■■■ｇ●ＢＧ■ＢＧ

内のり

▲

’

際:蕊 茎畠達3

し

図4－2

図4－1

bal･s in tension,

cir: yielding shEngth of
longinldmal baIs.

▼

columnﾄ』－1

垂■｡｡●●○●●◆◆●
p⑪Ccce◆◆●①●p■■●●■

問題4－2▲

F,I”｢a' Wf'ding

P卿

Pc,

一

Column section

Fig.4-1

Latemllbrce P●●令■の■■●●①●●●●●。●●句

columnll『一ウ■●■●■、ロ》■●ｑ●■心■ご■■■Ｃｄｃ丑Clear heightﾉ1

！

水平変形6

図4－3

QI: cross sectional area of

▲

61

6Cノ

柱の断面

6Cノ

Fig.4-2（15点）

Question 4-2 (15 marks)
鉄筋コンクリート柱の構
鉄筋コンクリート柱の構造性能に対する横補強筋の効果について，説明しなさい。
Explain the effect of lateral remfbrcement on stlucmral perfonnance of RC columns.

－9－

51

Fig.4-3

Horizontal

diSplaCement6

Queshon 5(1))٠ñ+ 35 ،‫(تى‬mımш-m¡ị:mf6Ύl[i๑\iVi:ţưJะề[

5

Answer the ‫؛‬.!lowing questions about vibration of struchires. (Subtotal 35 marks)‫·جتااظد‬im 5-1 (D 1l/٠:łf>،:7KI^3P(t) (/ ịiỆĩm) ^4-rmfòb(Dtf/jo iề

filj пг, ịụiệvik,‫لءخااا№'غا‬

Consider a horizontal force ۶(t) (t is time) acting on the one-mass system which models a building as shownin Fig. 5-1. Letting m be the building mass, k be the liorizontal stiffoess, c be the viscous damping coefficient,x(ịt) be horizontal displacement of the mass, answer the followingquestions.
mJ)‘0iŤčJj
Restoring For« with !temping Force

Pt“:‫؟‬Я

αωΑ
-A

Ε>
Η5-1

-kA

И5-2

Fig. 5-1 One mass system

(a)

X

A

Fig. 5-2 Relation between force and displacementljũềoimìýĩlẮ iýJ๑ệ^v)^[^-ẩẰ) ‫ج‬7‫„هةل‬
Represent the equation of motion (equilibrium of forces) of the one mass system,(b)ШţmแωtШแhţะm,c.kΘจ์iЬ‘^\ąP^ị๑^mЬ\X^h^ЪH tf:. (a)0|i
Represent the namral circular frequency ω and damping factor Λ using necessaty terms from m. c, k. Also,

rewrite the vibration equation of (a) to include ω and ‫لذ‬.

(c)‫أ‬€‫>غي‬7‫بتد‬١‫يرار‬٢‫—ت‬،Ofj ự)‫ال‬١‫اة‬:‫نهج؛ق‬Represent the equation of energy balance of the one mass system,(d)τΚ¥Ιίί:‫؛‬ίΛ:(0 = A €0ร(ฬ0ะ - Θ)P(t)> lXlMωo๑Ề|-åfũİ-ĩ:ÍẾ\|:ềะýìỂlŤ:lM{A nil, Θ ỈỈÍÍlIIì) ^ĩ:^ţiiьrıòь๑tfòω٥ = ω

(7)iiặ, ÌàtiM'ũ7íý3tịW-Ềiử.

^)‫؛‬٣‫م‬#١،‫[ة]ة‬:л;٧:5-2
ว

Let the horizontal displacement be given by χ(ί) = ^ C0s(w٥t — Ỡ) {A is constant, 0 is phase delay)
when exciting tlie one-mass system by stationary hannonic force witli circular frequency of a>0 as p(t).

When ω. = ω, the relationship between restoring force with damping force and horizontal displacement isgiven as Fig. 5-2.

(!) ‫ت!جج‬-‫مداأرج‬٠—íOiâ.ẤÌầrA,/،‫ة‬٠1‫ا‬١‫ب‬7٢١‫ه‬
Represent the maximum value of tire potential energy using A, k.

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(ii)一周期分の加振に対して減衰力のなす仕事を求め'C9の,Aを用いて示せ。
Represent the wolk by the damping fbrce in one cycle of excitation usmg c, (u, A .

(2)構造物の振動において，減衰とはエネルギーが逸散する現象と考えられる。減衰の物理的な要因について，例を複数挙げて説明しなさい。
Dampmg m vibration of strucmres is considered as energy dissipation phenomenon. Explain the physicalcauses of damping with two or more examples

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問題6

防災工学に関する以下の問に答えなさい。（計35点）

Question 6

Answer the fbllowing qUestions regarding disaster prevention engineering. (Subtotal 35 marks)

以下の災害を受けたときの建物被害の特徴について答えなさい。
Answer the characteristics of buildmg damage in the fbllowmg disasters(1)洪水(2)液状化

FIood

LiqUefaction of the ground(3)竜巻

Tbmado(4)地震Earthquake(5)豪雪Heavy snow

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