Fundamentals of Structural Analysis
Fundamentals of Structural Analysis
5th Edition
ISBN: 9780073398006
Author: Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher: McGraw-Hill Education
Question
Book Icon
Chapter 14, Problem 6P
To determine

Calculate all the reactions and draw the moment diagrams.

Expert Solution & Answer
Check Mark

Answer to Problem 6P

The vertical reaction at A is 57.42kips_.

The vertical reaction at B is 67.5kips_.

The vertical reaction at C is 13.08kips_.

The bending moment at A is 182.57kipsft_.

The bending moment at B is 120.85kipsft_.

The bending moment at C is 74.57kipsft_.

Explanation of Solution

Restrained structure: Clamp joint 2:

Show the free body diagram of the restrained structure as in Figure (1).

Fundamentals of Structural Analysis, Chapter 14, Problem 6P , additional homework tip  1

Refer Figure (1),

Find the fixed end moment of the member 1-2 (FEM12) using the relation;

(FEM12)=±wL212=±6×18212=±162kipsft

Find the fixed end moment of the member 2-3 (FEM23) using the relation;

(FEM23)=±PL8=±30×248=±90kipsft

Find the moment in clamp using the relation;

Moment in clamp=(FEM21)+(FEM23)=16290=72kipsft

Show the free body diagram of the restrained structure with FEM and moment as in Figure (2).

Fundamentals of Structural Analysis, Chapter 14, Problem 6P , additional homework tip  2

Show the free body diagram of the structure with unit rotation at 2 Figure (3).

Fundamentals of Structural Analysis, Chapter 14, Problem 6P , additional homework tip  3

Moments due to unit rotation at 2:

Find the moment at the member 1-2 using the relation;

(M12JD)=2EIL(θ)=2EI18(1)=EI9

Find the moment at the member 2-1 using the relation;

(M21JD)=2EIL(2θ)=2EI18(2×1)=2EI9

Find the moment at the member 2-3 using the relation;

(M23JD)=2EIL(2θ)=2EI24(2×1)=EI6

Find the moment at the member 3-2 using the relation;

(M32JD)=2EIL(θ)=2EI24(1)=EI12

Find the stiffness coefficient K2 using the relation;

K2=(M21JD)+(M23JD)=(2EI2)+(EI6)=7EI18

Find the rotation at joint 2;

Take summation moment about joint 2.

M2=0Mclamp+K2θ2=072+7EI18×θ2=0θ2=185.14EI

Find the moment at the member 1-2 using the relation;

M12=FEM12+θ2M12JD=162185.14EI×(EI9)=182.57kipsft

Find the moment at the member 2-1 using the relation;

M21=FEM12+θ2M21JD=162185.14EI×(2EI9)=120.85kipsft

Find the moment at the member 2-3 using the relation;

M23=FEM23+θ2M23JD=90185.14EI×(EI6)=120.85kipsft

Find the moment at the member 3-2 using the relation;

M32=FEM23+θ2M32JD=90185.14EI×(EI12)=74.57kipsft

Show the free body diagram of the beam as in Figure (4).

Fundamentals of Structural Analysis, Chapter 14, Problem 6P , additional homework tip  4

Refer Figure (4),

Consider AB:

Find the vertical reaction at A;

Take summation moment about B.

MB=0182.57+6×18×182120.85+Ay×18=0Ay=1,033.7218Ay=57.42kips

Thus, the vertical reaction at A is 57.42kips_.

Find the vertical reaction at B;

Summation of forces about y axis is equal to zero.

Fy=06×18+Ay+By=0108+57.42+By=0By=50.58kips

Consider BC:

Find the vertical reaction at B;

Take summation moment about C.

MC=030×12+120.8574.57+By×24=0By=406.2824By=16.92kips

Find the vertical reaction at C;

Summation of forces about y axis is equal to zero.

Fy=030+By+Cy=030+16.92+Cy=0Cy=13.08kips

Thus, the vertical reaction at C is 13.08kips_.

Find the total vertical reaction at B;

By=50.58+16.92=67.5kips

Thus, the vertical reaction at B is 67.5kips_.

Show the free body diagram of the beam as in Figure (5).

Fundamentals of Structural Analysis, Chapter 14, Problem 6P , additional homework tip  5

Refer Figure (5),

Shear force calculation:

VA=Ay=57.42kipsVBL=Ay6×18=57.426×18=50.58kipsVBR=50.58+By=50.58+67.5=16.92kipsVC=16.9230=13.08kips

Find the distance when shear force is zero (x):

Equate the equation of shear force to zero.

Vx=057.426x=0x=57.426x=9.57ft

Bending moment calculation:

MA=182.57kipsftMmax=182.57+6×x×x2=182.57+6×9.57×9.572=92.18kipsft

MB=120.85kipsftMBCcenter=182.57+57.42×306×18×(182+12)+67.5×12=82.03kipsftMC=74.57kipsft

Thus, the bending moment at A is 182.57kipsft_.

Thus, the bending moment at B is 120.85kipsft_.

Thus, the bending moment at C is 74.57kipsft_.

Show the shear force and bending moment diagram as in Figure (6).

Fundamentals of Structural Analysis, Chapter 14, Problem 6P , additional homework tip  6

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A simply supported beam is subjected to the end couples (bending is about the strong axis) and the axial load shown in the figure below. These moments and axial load are from service loads and consist of equal parts dead load and live load. Lateral support is provided only at the ends. Neglect the weight of the beam and investigate this member as a beam-column. Use Fy that P40 k and M = 68 ft-k. For W10 × 33: I = 171 in.4; 10 ft and C₁ = 1.0: Mn = 134 ft-kips and Mn/₁ = 89.3 ft-kips; = 50 ksi. Suppose for Lb for Lc - = 10 ft: Pn 330 kips and Pr/c = 220 kips. W10 X 33 P M M 10' Pu A) + Ферп 9 a. Use LRFD. Select the interaction formula: Mur 84, Mnz Muy + <1.0 Фь Мпу Pu Mur Muy B) + + ≤ 1.0 20c Pn Фь Мих nx ФоМпу -Select- ✓ Compute the interaction formula. (Express your answer to three significant figures.) -Select- 1.0 This member is -Select- b. Use ASD. Select the interaction formula: Ра 8 Max May A) + + <1.0 Pn/c Mnx/b Mny/b Pa Max May B) + + 1.0 2Pn/c Mnx/b Mny/b -Select- Compute the…
Determine whether the given member satisfies the appropriate AISC interaction equation. Do not consider moment amplification. The loads are 50% dead load and 50% live load. Bending is about the x axis, and the steel is ASTM A992. Suppose that P = 280 k. For W12 x 106 with Fy = 50 ksi and Lc = 14 feet: Ферп 1130 kips, Pn/Sc = 755 kips, Mn = 597 ft-kips, Mn/₁ = 397 ft-kips. P 240 ft-k W12 X 106 14' K₁ = Ky = 1.0 240 ft-k a. Use LRFD. P Determine the factored axial compressive load and the factored bending moment. (Express your answers to three significant figures.) P₁ = Mu = kips ft-kips Select the interaction formula: P₁ A) + Мих Muy + ≤1.0 Ферп 9 Фь Мих of Mny Pu Мих Muy B) + 20c Pn Mnz + <1.0 Фь Мпу -Select- Compute the interaction formula. (Express your answer to three significant figures.) -Select- 1.0 This member -Select- b. Use ASD. the AISC Specification. Determine the total axial compressive load and the maximum bending moment. (Express your answers to three significant…
Refer to the following figure: K 6 m T 0.25 H 0.75 H 1 m A c,O,Y 3 m B 2 m 1 m C Figure Peck's (1969) apparent-pressure envelope for cuts in soft to medium clay Given: y = 17.5 kN/m³, c = 30 kN/m², 6 = 0, and center-to-center spacing of struts in the plan = 5 m. Determine the sheet-pile section modulus for the braced cut. Use all = 150 MN/m². (Enter your answer to three significant figures.) S = ×105 m³/m
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Structural Analysis
Civil Engineering
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:Cengage,
Text book image
Structural Analysis (10th Edition)
Civil Engineering
ISBN:9780134610672
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Principles of Foundation Engineering (MindTap Cou...
Civil Engineering
ISBN:9781337705028
Author:Braja M. Das, Nagaratnam Sivakugan
Publisher:Cengage Learning
Text book image
Fundamentals of Structural Analysis
Civil Engineering
ISBN:9780073398006
Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:McGraw-Hill Education
Text book image
Sustainable Energy
Civil Engineering
ISBN:9781337551663
Author:DUNLAP, Richard A.
Publisher:Cengage,
Text book image
Traffic and Highway Engineering
Civil Engineering
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Cengage Learning