Math Problem Statement

1. Batang ABCD seperti yang ditunjukkan pada gambar di bawah ini memiliki bagian-bagian dengan penampang lintang yang berbeda-beda dan menerima beban aksial. Batang ini terbuat dari aluminium yang memiliki nilai modulus elastisitas 70 GPa. Tentukan perubahan panjang yang terjadi pada setiap bagian batang AB, BC, dan CD. 2. Batang-batang pada rangka batang (truss) yang ditunjukkan pada gambar di bawah ini memiliki luas penampang lintang yang sama yakni 8 mm^2. Jika tegangan normal maksimum rata-rata pada batang AB dan CB tidak boleh melebihi 140 MPa, tentukan besar beban P maksimal yang dapat diterapkan pada rangka batang ini.

Solution

The image shows a mechanical engineering problem with two questions, each related to axial forces and truss analysis. Here’s a breakdown:

  1. Question 1:

    • Beam ABCD: The beam has different cross-sectional areas and is subject to axial loads.
    • It asks to determine the change in length for each section of the beam (AB, BC, and CD).
    • Material: Aluminum with a modulus of elasticity (E) of 70 GPa.
    • There are axial forces applied: 5 kN at one end, 24 kN and 15 kN along different segments.
    • The cross-sectional areas are provided for each section (AB, BC, CD).

    The

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Math Problem Analysis

Mathematical Concepts

Axial Load
Elasticity
Stress and Strain
Truss Analysis

Formulas

ΔL = (F * L) / (A * E)
Stress = Force / Area
Strain = ΔL / L

Theorems

Hooke's Law

Suitable Grade Level

Undergraduate Engineering

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