Add the class always-open to your navbar and then use the following CSS:
<!-- language: lang-css -->
.navbar.always-open {
    border-radius: 0;
}
.navbar.always-open .navbar-header {
  float: none;
}
.navbar.always-open .navbar-toggle {
  display: block;
}
.navbar.always-open .navbar-collapse {
  border-top: 1px solid transparent;
  box-shadow: inset 0 1px 0 rgba(255,255,255,0.1);
}
.navbar.always-open .navbar-collapse.collapse {
  display: none!important;
}
.navbar.always-open .navbar-nav {
  float: none!important;
  margin: 7.5px -15px;
}
.navbar.always-open .navbar-nav>li {
  float: none;
}
.navbar.always-open .navbar-nav>li>a {
  padding-top: 10px;
  padding-bottom: 10px;
}
Example HTML:
<!-- language: lang-html -->
<pre><code><nav class="navbar navbar-inverse <b>always-open</b>">
    <div class="navbar-header">
        <a class="navbar-brand" href="#">Brand</a>
        <button type="button" class="navbar-toggle" 
                data-toggle="collapse" data-target=".navbar-collapse">
            <span class="icon-bar"></span>
            <span class="icon-bar"></span>
            <span class="icon-bar"></span>
        </button>
    </div>
    <div class="navbar-collapse collapse">
        <ul class="nav navbar-nav">
            <li class="active"><a href="#">Home</a></li>
            <li><a href="#about">About</a></li>
            <li><a href="#contact">Contact</a></li>
        </ul>
    </div>
</nav>
</code></pre>
Screenshot:

*Adapted from this bootply
BTW, if you're building your own version of Bootstrap with less:
You can just alter the @grid-float-breakpoint from @screen-sm-min to 999999999px