Name: truss force analysis at joints a to e
Uploaded: 2023-09-22T11:49:24.000Z
Duration: 1 min 30 s
Channel: JoVE

חשבו על מבנה טרוס עם מפרקים נטולי חיכוך המקובעים לקיר ותמיכת רולר על הקרקע. אם כוח של 150 N מוחל על מפרק A, ואז לקבוע את הכוחות בכל איבר של truss.
ניתן לקבוע את הכוחות בכל מפרק באמצעות שיטת המפרקים.
ראשית, ניתן לקבוע את הזווית בין האיברים AC ו-AB כהופכי השיזוף של היחס בין אורך BC ו-AB.
שנית, ציירו תרשים גוף חופשי של מפרק A ופתרו את הכוחות למרכיביהם. על ידי יישום משוואות שיווי המשקל, ניתן לקבוע את הכוחות הבלתי ידועים.
לאחר מכן, על ידי ציור דיאגרמות הגוף החופשי של המפרקים B ו- C, ובאמצעות משוואות שיווי משקל, ניתן לקבוע את הכוחות הבלתי ידועים במפרקים B ו- C.
לבסוף, צייר תרשים גוף חופשי של המפרקים D ו- E. עבור חברי CD ו- EF, פתור את הכוחות לרכיבים האופקיים והאנכיים. הכוחות הבלתי ידועים במפרקים D ו-E ניתנים לקביעה באמצעות משוואות שיווי משקל.

<ol>
	<li>היבלר, R.C. (2016). מכניקה הנדסית - סטטיקה ודינמיקה. הובוקן, ניו ג'רזי: אולם פירסון פרנטיס. עמ' 276-277.</li>
</ol>

לא הוכרז על ניגוד עניינים.

שיטת המפרקים: פתרון בעיות ii

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חשבו על מבנה מסבך עם מפרקים נטולי חיכוך קבועים לקיר ולתמיכת רולר. אם מופעל כוח של 150 N על מפרק A, ניתן לקבוע את הכוחות בכל איבר של המסבך באמצעות שיטת המפרקים. <img alt="Figure 1" src="/files/ftp_upload/14283/14283_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> 

ניתן למצוא את הזווית בין האיברים AC ו-AB על ידי לקיחת הטנגנס ההפוך של היחס בין האורכים של BC ו-AB, והתוצאה המתקבלת היא 67.38°. דיאגרמת גוף חופשי של מפרק A מחושב, וכל הכוחות הלא ידועים נפתרים למרכיביהם המתאימים. 

לאחר מכן ניתן להשתמש בתנאי שיווי משקל הכוח האנכי כדי לחשב את הכוח הפועל על איבר CA, השווה ל-173.08 N. <img alt="Equation 1" src="/files/ftp_upload/14283/14283_PT_Equation_1v2.svg" style="text-align: center; height: 15px;"> 

באופן דומה, ניתן להשתמש במצב שיווי משקל הכוח האופקי כדי למצוא את הכוח FAB כ-161.54 N. <img alt="Equation 2" src="/files/ftp_upload/14283/14283_PT_Equation_2v2.svg" style="text-align: center; height: 15px;"> 

דיאגרמות גוף חופשי של מפרקים B ו-C נחשבים, ותנאי שיווי משקל הכוח האנכי והאופקי מיושמים כדי לחשב את הכוחות הלא ידועים FBD , FCD , וFEC. הערכים המתקבלים עבור FBD , FCD , ו-FEC הם 161.53 N, 173.08 N ו-207.70 N, בהתאמה.

דיאגרמות גוף חופשי של מפרקים D ו-E מחושבים לבסוף, ותנאי שיווי משקל הכוח האנכי והאופקי מיושמים. זה נותן את הערכים של FED וFDF כ-138.46 N ו-265.39 N, בהתאמה.

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שיטת המפרקים: פתרון בעיות II

שקול מבנה truss עם מפרקים ללא חיכוך קבוע קיר ותמיכה רולר. אם כוח של 150 N מוחל על מפרק A, הכוחות בכל ...

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JoVE Core

Mechanical Engineering

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Unit 1

יחידה 1

Structural Analysis

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KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

Method of Joints: Problem Solving II

truss force analysis at joints a to e

Truss force analysis at joints A to E uses the method of joints to find the force in each member. The truss has frictionless joints, a wall support, and a roller support. A 150 N force is applied at joint A, and the member forces are solved from joint to joint.

First, the angle between members AC and AB is found using the inverse tangent of the ratio of BC to AB. This gives an angle of 67.38°. A free-body diagram of joint A is then drawn, and each unknown force is split into vertical and horizontal components.

The vertical force equilibrium equation is used to find the force in member CA, which is 173.08 N. The horizontal force equilibrium equation gives the force in member AB as 161.54 N. Free-body diagrams for joints B and C are then used to continue the calculation.

At joints B and C, the vertical and horizontal equilibrium conditions are applied again. This gives FBD = 161.53 N, FCD = 173.08 N, and FEC = 207.70 N. Free-body diagrams of joints D and E are used last, and the same equilibrium steps give FED = 138.46 N and FDF = 265.39 N.

Truss Force Analysis at Joints A to E

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method of joints: problem solving ii

Truss force analysis at joints A to E uses the method of joints to find the force in each member. The truss has frictionless joints, a wall support, and a roller support. A 150 N force is applied at joint A, and the member forces are solved from joint to joint. First, the angle between members AC and AB is found using the inverse tangent of the ratio of BC to AB. This gives an angle of 67.38°. A free-body diagram of joint A is then drawn, and each unknown force is split into vertical and...

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Truss Member Force Calculation by Sections

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Space Truss Forces and Stability

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3D Truss Force Analysis with Joint Equilibrium

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frames

Frame Analysis in Structural Systems

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machines

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Toggle Clamp Force Analysis

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key terms and concepts

Use the method of joints to solve truss forces at joints A to E. Find member forces from free-body diagrams, angles, and equilibrium equations.

Truss Force Analysis at Joints A to E | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Truss Force Analysis at Joints A to E

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