Môn hình họa có lẽ là một môn học mà sinh viên ngành kiến trúc thường gặp khó khăn trong lúc học vì tính phức tạp của nó, đặc biệt là phần vẽ mái nhà. Thời chúng tôi là sinh viên cũng thế, gặp các bài tập vẽ mái dốc giao nhau là chúng tôi rất sợ vì tìm ...

Introduction

The roof is the backbone of the house. In descriptive geometry, we use lines and angles to determine roofline, peak line, hip, pitch of a roof. A roof shape has a wide variety of configurations which differ greatly from region to region, depending on...

Chapter 1: Framing Roof Geometry by Bisector Method

A frame section of a typical A-frame roof, in geometry, is an isosceles triangle.In plan, refer to Image 1 - Roof Plan below, if we extend rooflines until they intersect, we have isosceles triangles, where roof peak lines are bisector KJ and bisector FH.To facilitate this roof framing study, below are the mathematical terms used in geometry.Roofline - an outline or outer edge of a roof.(ABCDEG.A)Peak Line - a horizontal line running the length of a roof where the two sloping sides meet at highest point on a roof. In this case, it is the plan projection of the intersection line which is also a bisector.KJ = (KJBAF∩ KJCD) FH = (FHEDK ∩ FHGA)Hip - an intersection line of two adjacent sloping sides of a roof.AF = (AFKJB ∩ AFHG) KD = (KDCJ ∩ KDEHF) JC = (JCB ∩ JCDK)JB = (JBAFK∩ JBC) HE = (HEG ∩ HEDKF) AF = (AFHG ∩ AFKJB)Pitch or Slope - a measure of a roof steepness(JM ⊥ CD) (JM’ ⊥ CB) (JM’’ ⊥ BA)Bisector points - points belonging to the roof top line (bisector)(J - K -F - H)An apex - the highest point or the tip where belongs to the angle opposite to the base, known as the vertex angle.

Application Exercise #1

Please complete this framing structure of the roof below. Apply bisector of an isosceles triangles strategy and use these rooflines (A2B2C2D2E2G2H2K2) as a starting point. See Image 2 below for reference.Step 1 - Extend the rooflines to form the vertex angles. See Image 3.Step 2 - Draw bisectors accordingly to those isosceles triangles. See Image 4.Step 3 - Complete the bisectors of those rooflines, also known as roof peak lines in this case. See Image 5.Step 4 - Connect bisector points and draw peak lines, and hips. See Image 6.Step 5 - In section, draw roof slopes accordingly. See Image 7.Application Exercise #2Application Exercise #3Application Exercise #4The use of 45-degree grid lines for a typical type A-frame. See Image 10.In construction, we often see single-family houses having typical hip and gable roof (A-frame) where the rooflines are parallel and perpendicular. In this case, we use 45-degree grid lines to locate Rooflines, Roof Peak Lines, Hip, and Slopes.Step 1 - Giving the system of parallel and perpendicular rooflines, please construct this roof by using 45-degree gridlines or use 45-degree ruler.Step 2 - Use 45-degree gridlines or ruler to draw the median lines of triangles. Or use compass technique to construct the bisectors.Step 3 - Draw Peak Lines, and Slopes. See Image 13.Step 4 - Draw this roof in sections with Rooflines, Peak Lines, and Slopes [1] An isosceles triangle is a triangle that has two sides of equal length.